Back a couple seasons ago there were clear champion picks and comps you could draft, and most were viable. I think I'm remembering a patch or so before the Juggernaut update. It was bliss.
Top lane, you could pick what you wanted; Something like Jayce/Renekton for early game comps, Vlad/Rumble for carry oriented mid-game focus, or tanks for the late game teamfights. The choice mattered to fill a gap within your team comp, or if you were an early pick, could choose to be the teams carry.
For Jungle you could fill the gaps where you needed it; AP, AD, Bruiser, Tanky, you could play it all and still be useful if you played well. If you played a tanky jungler, it wouldn't matter if you got invaded because you had the raw stats to survive long enough for your team to come back you up. If you had a volatile matchup somewhere, you could pick an early game champion like Lee and be there to help faster at the sacrifice of being outscaled late game.
Mid lane; Too much AP in Vlad top and Grag jungle? Team relies on late game heavily? Need some late game? Need some burst? Need some extra CC? We got it all here, as long as it does damage and waveclear it has a home mid lane. Not everything here was META of course, but not many picks were entirely useless either because they had their strengths and weaknesses.
ADC; Team drafted carries? Grab some utility in Ashe, Varus. Wombo-Combo heavy team? Twitch/MF. No late game threats? You've got your choice of hypercarries. Facing a bunch of divers? Ez/Lucian/(Pre RW)Graves. You have your choice of picks with clear strengths and weaknesses. META here is really dependent on your team comp unless something is busted beyond belief (Kog/Lulu ardent meta).
Support; Lacking some tanks? Need some peel for your carries? No engage? No disengage? Too many tanks? You literally have so many options to choose from here, you can play to your own playstyle.
What's the state of the game right now? Whoever can get their cooldowns off first of course! Bursty, mobile carries are everywhere. Tank stats don't matter because Riot's philosophy of the game is that offense should outscale defense, the only time it matters is if you get fed and can become tanky before carries get damage. If you compare a full build tank to a full build carry, the carry can usually dispatch the tank within seconds.
Now obviously it makes sense that a carry can kill a tank you say! Well of course it makes sense, but what's the point of building tanky if you cannot lock down this carry long enough for YOUR carries to come kill them. As a tank, you should be living long enough to get multiple rotations of your cd's off in a teamfight. That's how tanks generate threat in a PVP game, CC/Disruption, since most players are smart enough to realize putting dps into a tank isn't worth it. Unfortunately, this is not the case in recent seasons. CC has been reduced and TTK has decreased, leading to a tank not being actually tanky enough to survive long enough to dish out multiple rotations in a teamfight. Tanks have been phased out by bruisers because damage is the only thing that counters damage, and Riot has been solidifying this mentality by buffing tanks DAMAGE instead of touching their CD's or CC duration.
During champ select, you used to have to think about the comp you were drafting. If you had no late game, you were hoping you could get a lead early and roll with it. All AD/AP team was basically an autoloss because tanks were tanky and having full Armor/MR was a godsend for tanks. Not having an early game made your team a pushover when it came to neutral objectives. Not having peel made the carries have to play incredibly safe. Not having a tank meant having a teamfight disadvantage. Champion picks didn't matter as much as it does now as long as you could fill a role your team needed and your target selection was good. Every champion had their time in the spotlight because games lasted 40-50 minutes, long enough for each champion pick to make an impact in their designed powerspike and reach full build if the game hadn't been taken over already.
Nowadays players can decide games from champ select a majority of the time. Champs keep getting into a broken state because of some balance patch and the only way to deal with the problem is to kill that champion because tanks can't lock them down long enough for carries to kill them. It used to be good advice to build tanky when behind, but now it doesn't even matter when you can be 0/3 with a giants belt/armor against a tiamat/phage or something and still be killed under your t2.
Remember when Nautilus top lane was a threat because he could snag a carry and keep them locked down long enough and not because he could hit you for 1/3 to half of your HP with a combo? Remember when teamfights were decided based on target selection, catches, lockdown, and peel rather than a single misstep from one of your carries? Remember when your lane wasn't decided at 1 or 2 kills? Remember when you had to think about what cooldowns you needed to use at what time on the proper target instead of mashing your face on the keyboard as fast as possible?
I do, and I want it back. With the introduction of Nexus Siege, the state of the game perfectly matches what that mode is designed to do. Imagine how boring Nexus Siege would have been if introduced back in season 3/4, it just doesn't fit the mentality that state of League was balanced around.
Champion picks are more meaningful than the roles that they were designed to cover, tanks can't be a threat long enough for carries to get involved, damage counters damage instead of tank stats doing that job, and full builds are rare on all champs when some of them are still balanced around this (or some have been rebalanced to not be attached to this).