There is a reason massively dash heavy champions, like Akali or Irelia, can be so well played in Pro Play despite pro play revolving heavily around positioning, macro, etc, while in low elo, where it's supposedly a one-shot fiesta, champions like Irelia struggle heavily. A lot of this has to do with skill cap, and how a champion's kit is heavily revolved around a single ability to play to their max potential, but that's not the only problem.
I will be looking at the two most important types of mobility, and will be ignoring other forms, like base movement speed, movement speed modifiers, and forms of counter-mobility, such as slows, cc, etc.
There are two kinds of mobility. Micro and Macro. Macro comes in the form of things like Aurelion Sol, with his "I pressed E now I'm ganking bot" button, or Twisted Fate's "Here's a 5500 range stun for my ult". Micro comes in the form of things like Irelia's Q, a targeted dash which makes her stronger the more she uses it, which can be used more than 8 times in a 1v1 situation with a single full minion wave, regardless of whether there is a cannon minion or not, in a single spell rotation.*(For the non-believers, I have the combo at the bottom.) Talon is a champion that is a mix, with an E that lets him vault up to 800 units over walls on a 2 second cooldown.
With these champions, it's never enough to just have the mobility. Twisted Fate reveals all enemy champions. Aurelion Sol can see over walls and has a passive with his E that allows him to gank effectively even without his E. Irelia not only has a heal on the dash, but also has bonus damage to minions, resets its cooldown upon death of a target, and procs on-hit effects.
When a champion has an overbearing form of either micro OR macro mobility that requires a heavy tradeoff, whether that be through the champion's kit or itemization effectiveness, they become overbearingly powerful in high elo, while low elo may not find as much use for it. This is because in high elo, players know HOW to use that mobility to make it worth the tradeoff. This is why teleport is so heavily taken in high elo, while in low elo, Ignite is the summoner spell of choice. In the case of Flash, NEARLY NO tradeoff is required, due to the instantaneous aspect of Flash.**
Let's look at Twisted Fate. Twisted Fate sacrifices a lot of reliable burst in exchange for a 5500+ ranged stun on a 2+ second delay (accounting for projectile AA speed). His Q is hard to properly aim at long ranges, and his E requires careful planning for a lackluster damage spike. What does he get in exchange? He gets the ability to be versatile with his W. Why is the massively reduced 1v1 potential worth it? His ultimate is essentially a Teleport without needing a target, and the reason it's powerful is because pros can easily determine when that single stun is enough to turn the tide of a skirmish. However, overall he's balanced, because it's highly telegraphed, and is easily out playable, and he sacrifices a relatively large of his organized teamfight power in exchange for ganking dominance.
Compare that to Irelia. The amount of micro-mobility she has allows her to effectively waveclear quickly, while gaining power at the same time. With the recent nerfs, she's going to go to the gutter. Or is she? Despite the heavy nerfs on her, she's still a viable pick in High Elo, because the amount of mobility that can be capitalized on is insane. An ultimate that allows teamfight potential, an E that is an AOE stun that's hard to land, a Q that heals and increases your attack speed, and at 5 stacks increases your damage, and a W that'll reduce physical damage by 50%. Granted, Irelia is much more matchup dependent now, but she still has many tools at her disposal that Twisted Fate can only gawk at. However, she's gated by her weak damage and reliance on actually landing these abilities, primarily her Ultimate, while Twisted Fate is reliable.
Why are Talon and Yasuo, two champions with massive amounts of mobility, still played with success in both low AND high elo?
In the case of Talon, he's self sufficient to the point of being able to 1v1 many champions reliably, but his mobility allows for high elo plays as well. He is gated by the fact that many players will use his E incorrectly/put themselves in a bad spot position-wise. Talon's form of mobility is unique, and doesn't always lead to a better position. This is why he is played both in low AND high elo, despite still being more prominent in high elo. His tradeoff is the situational usage of his E, and the planning it requires.
In the case of Yasuo, he's one of the most iconic League of Legends champions, second only to perhaps Ahri, and is not gated by the potential of his kit, but rather by the skill of the player. With the damage of 2 ADCs at the expense of range, his skillcap is so insanely high that Riot has reduced the bar, so that there is no NEED to play Yasuo at the same potential as Irelia. In the case of Irelia, she can't match Yasuo's damage. In exchange, she gets more dashes onto single targets. What good is micro mobility when you don't have the damage to back up the mobility? Especially in the case of Yasuo, he also has several tools Irelia doesn't. Irelia can negate all physical damage by 50% for a short duration, while Yasuo can negate all projectiles with a large aoe wall that extends to teamfights, and has an ultimate that is extremely powerful with good team picking.
With players who know how to play around Yasuo's E's micro mobility, they begin to find success in countering him, until they reach the "macro" aspect of his mobility. His ultimate extends the knockup duration of any knockup by 1 second. Highlighting the indicator of his ultimate, the actual AOE circle is VERY LARGE. In addition to that, he gets 50% armor penetration for a duration, but the cc and repositioning alone would be enough to make many cry. He's hated because there is always a way he can outplay you, whether it be through a 1v1 or reliance on team members. The only issue is if the PLAYER behind Yasuo is good enough to do so.
There is no tradeoff for Yasuo, but there often appears to be. His E can't be used to dash to the same target for 5 seconds. However, when comparing that to Irelia, understand that Irelia brings less damage, less sustain, and less teamfight potential to the table, and she can't dash to minions again either, because either they'll be dead, or her Q will be on cooldown. Both have their uses and personal problems, and patch by patch power will have an effect on how good they are.
We have looked at the tradeoffs that different champions have. Let's revisit that one-dimensional quotation I used. "Aurelion Sol, with his "I pressed E now I'm ganking bot" button", "Twisted Fate's "Here's a 5500 range stun". "Irelia's Q, a targeted dash which makes her stronger the more she uses it, which can be used more than 8 times in a 1v1 situation with a single full minion wave, regardless of whether there is a cannon minion or not, in a single spell rotation.", "Talon is a champion that is a mix, with an E that lets him vault up to 800 units over walls on a 2 second cooldown."
Each champion has a tradeoff, whether it be damage, reliability, skill cap, or positioning unreliability. Pros can take that tradeoff and be satisfied. The average player cannot. Our strategies in lower elos rely on the basic triangle of Burst > Sustained > Tank > Burst. With the amount of mobility, our balance is being thrown off. During a game, we aren't going to use Yasuo's ult consistently in teamfights. We're going to use it in a 1v1, then complain about how Yasuo's ult didn't put/put him under the turret's firing range, not complain about how 1 second of reliable additional cc is actually disgustingly powerful when taken advantage of.
Am I going to play Irelia mid, or am I going to play Malzahar, the Prophet of the R button, in midlane? I don't know how to use mobility to negate the damage and trade effectively. I'm going to stick with Malzahar, despite the easy counter of a QSS.***
TL;DR: Mobility, both micro and macro, have a lot to do with how a champion is viable in high elo vs low elo. What seperates high and low elo is whether that mobility is going to be worth the tradeoff in the rest of the champion's kit / available build items.
*Irelia's method to achieve over 8 dashes is as follows: Q>Q>Q>Q>Q>Q onto the minions, provided they are within the health threshold. R > Q > E > Q onto enemy champion. Last Q is the second gapcloser. With this method you have a reliable way of sticking to the same enemy champion 3 times for a total of 9 dashes, not including ganks, cannon minions, or larger minion waves due to freezing etc., and you'll also have max Ionian Fervor stacks, with 40% bonus attack speed and bonus damage on-hit.
**Flash is the universally most used summoner spell due to its instantaneous effect, as well as the potential for damage, negation of damage, and mobility. If Flash were replaced with Hexflash, that would be interesting, but ultimately the game already revolves around Flash, and immobile champions who do not have the tools to unload their kit's potential must rely on Flash to do so. Exhibit 1: Annie. Exhibit 2: Malzahar. Some champions who already have enough micro mobility, such as Shaco, who won't lose as much as they gain with the tradeoff of Flash for Ignite, or with champions with external factors, like Teemo's constant stealth and movement speed allowing him to effectively take Ghost into certain matchups, are all valid reasons for not taking Flash.
***There are certainly people who hate Malzahar for his point-and-click mechanic of a 2.5 second suppression. I find it stupid how he was reduced to a literal R button. His Q is the only aspect of his kit that remains interesting to me due to how it's aimed. However, I'm talking about practicality. Most Irelia players who don't main her will lose almost any matchup in midlane, because range is powerful when there is no knowledge of how to manipulate a situation to your advantage with mobility. In Irelia's case, she could easily E>Q>Q onto an enemy champion once reaching max stacks of Ionian Fervor on minions. However, she will have likely taken more damage than her Q's heal could have mitigated through the rotation of abilities most midlaners posses.