> esports ultimately resulted in barbaric desecration of formerly-enjoyable multiplayer experiences
This I agree with
> Starcraft 2 and LoL evolved into some of the top offenders in this
This I couldn't disagree more. Especially Starcraft 2 is the worst example you could have picked. The game has such a high skill ceiling that you can get away many playstyles until you hit the uppermost ranks. As a master player myself (the rank, I'm far from being a "master" at Starcraft 2) I can comfortably hold myself in Diamond league without microing or even looking at my units or even with only building/using a single unit type and crazy compositions. I got pretty low apm, and my playing looks nothing like that of a pro player (which does resemble your description of one handed organ/piano playing [1]).
"Meta" in a game like that only applies to people in upper Grandmaster and Pro territory, and in a Game like Starcraft 2, a low Grandmaster player and a pro player are very far apart from each other. It's not something the devs force upon you, it's what you have to familiarize yourself with to reach a certain level of gameplay. Now where that level lies is something the devs can influence.
What I just described applies to many 1v1 competitive games, take a look at fighting games too.
You basically imply that Starcraft 2 went wrong somewhere to please e-sports, but are you familiar with high level Starcraft 1? It's way more ridiculous in every aspect of the game and on top of the high skill ceiling you have to familiarize yourself with many quirks of the game to become a decent player, which makes it harder and less accessible in general, but the skill ceiling was just as high or even higher than that of Starcraft 2.
> League of Legends
This is a more appropriate example, because here you are getting forced into certain meta compositions and picks very early on. However this is as much a community problem as it is a dev problem. At no point is there any need for mid level LoL players to follow "the meta", but the community is very obsessed with following what "the pros" do, whether or not that makes sense.
> I can play [insert role] all day on 1 server with other humans and no one will give me shit about it.
Honestly I believe one of the main problems you are describing is matchmaking rather than game balancing. With modern style MMR/Elo ratings in team based multiplayer games, playing online is in general way less relaxed than the "good old" joining a server and chilling there with players of vastly different skill levels, which is part of what enables many unconventional playstyles.
The development of meta in general is inevitable if you match players based on their skill and give them access to forums and the ability to share knowledge. However as I said initially, I generally agree that quite a few multiplayer games were ruined by devs chasing "e-sport" status.
And I absolutely agree that multiplayer games that allow for many different playstyles are more fun, but they are also way harder to create and balance, and the community will find optimal strategies and overpowered characters even if you as the dev do not.
[1]: https://youtu.be/SAo3QwnPruc?t=281