So I'm sure that lots of people have their own answer to this question, but I wanted to toss my own hot take into the ring before throwing the discussion to the hungry balance wolves.
In a categorical, systemic sense, League can be boiled down to a series of strategy checks and skill checks. From a single player's perspective, they are making a great amount of informed decisions based on a volatile array of information, such as teammate positioning, enemy spells, and HP values. Making good decisions and executing them well leads to victory; making mistakes and having them punished leads to defeat. This is something we accept whenever we play the game, and is something that we can agree that League's design and balance should reflect at all times.
I would assert that "counterplay" comes in the form of a combination of strategy checks and skill checks. For example, counterplay to Lux's Q snare could come in the form of walking out of the way of the skillshot (skill), spending a cooldown to block or dodge the ability (strategy+skill), or simply not being in range of Lux until she spends her Q cooldown (strategy). Skillshots are a *somewhat* cheap form of introducing visible, skill-check counterplay, but they are successful at doing so because they introduce the aim/dodge dichotomy.
Any PvP game with skill checks involves two factors: those who introduce the skill check (aim) and those who undergo it (dodge). Aiming can be considered itself a skill check, using movement or ability prediction to compete with the dodger directly. In order to make these skill checks fair, Riot has added visual clarity to skillshots, making it so that those who are targeted by the skillshot are empowered to know exactly how to dodge, even if they have not encountered the ability before. Thus, skill checks like aim/dodge can be considered visible counterplay: Getting struck by abilities is bad, and getting hit by as few abilities as possible is good. From there, you can also introduce basic strategy elements, like immobilizing enemies so that they cannot dodge, or positioning behind obstacles or out of vision so that enemies cannot aim.
The obvious opposite of visible counterplay is invisible counterplay - the strategic component. As I noted, some of this is present in regular, visible skill checks. Matlife's famous predictive Thresh hook is an example of this combination. But what exactly is the counterplay to an opponent who predicts your movement so well that you cannot use it to escape? Well, it's *invisible.* Stand out of range of the hook. Place minions and allies in the way to prevent Thresh from pressuring you with his hook. Use movement abilities in unpredictable, suboptimal directions.
Some champions, like the reworked Irelia, have little to no visible counterplay, although they do have plenty of invisible counterplay. Waiting for her to use her abilities to deny resets, using CC abilities to prevent her from using her full combo on her intended target, and playing around her ultimate cage are three great ways to keep Irelia in check. However, it's basically impossible to dodge her ultimate or her E when she uses it - at least, without spending cooldowns like Flash to do so (which is also strategic/invisible counterplay that Irelia can play around by either baiting out those cooldowns at a previous time or simply keeping track of when they are used).
I will assert for your consideration that Riot uses statistics and math to balance their game, which leads to an over-reliance on invisible counterplay for balance. And for clarity, yes, invisible counterplay is *far* more important than visible counterplay, and does make the game more fun and engaging. However, removing skill checks from the design of a champion means they are naturally on a superior footing to champions who are forced to introduce outplayable skill checks to their opponents.
With all this said, I do think that champions with 100% strategic or 100% mechanical counterplay have a place in the design of this game, and introduce volatility into the style of game played. However, they need to be balanced with this in mind. Akali and Irelia were very obviously balanced with the concept that enemies would learn to dodge and play around their abilities, and I think Riot was caught off guard by the fact that players were able to engineer situations where their ultimates or skillshots could be considered undodgeable.
Thanks for coming to my ted talk, riot pls hire me B)