I don't think Seasons 1-3 was any more balanced than the game is now.
So, hear me out, because this is sort of a theory post rather than any concrete, factual info.
Many people point to Season 1-3 as the "prime" of league. The most balanced time with the most champion picks, the most divversity, whatever have you. I'd like to challenge that but not from a mechanical standpoint. I'm not going to argue "Oh Season 1-3 was WORSE" or that Seasons 4 and beyond were balanced masterpieces but rather, I want to focus on the biggest change: The players.
Season 1-2 was one of the earliest ages of League of Legends. It was the genesis of the meta. It was the point where the League we know today took a rough shape. Again, bear with me. It was a wild, unknown time where everything was viable...because nobody TRULY understood how the game worked and what was strong. Take for example, GP/5 items. For the longest time, people laughed them off. They were something you picked up if you couldn't CS because you suck at the game haha so fany. Then people realized if you can CS and grab a GP/5 item, your gold income skyrocketed. And it stacked.
Even pros, in the infancy of the game, were still new to the inner workings of League. Take this clip for example:
https://www.youtube.com/watch?v=TmJvKx1n8TE
Scarra -loses his mind- when he sees someone pull off an insec for the first time. These days, if you can't do that, you shouldn't be playing Lee Sin at a high-tier level. There were so many small but major things nobody knew about the game from pros to noobs. I don't think League was any better or worse; We only thought it was more balanced because we earnestly knew so little about the game that we were missing major broken things in the game.
Of course, there's no way I can prove this. The obvious way would be to send a pro team today back to the days of S1/S2 but time travel is a messy and sloppy thing. But rather, consider it a possibility. Maybe League always had these problems and maybe League always had some gross imbalances. To quote that cartoon about the depressed horse:
"When you look at the past through rose-tinted googles, all the red flags just look like flags."