The root of all evil

Uhm, a bit ballyhoo, agree.

But I think it is a big problem that you can play here simultaneously all the time.

You can start games when other games are not completed. It is a basic feature but it is also the main source for misuse.

One should separate single game mode (Bullet, Blitz, Rapid) and sim mode (Corr, Simultaneous exhibitions).

In single game mode you have to close the game and accept resignation otherwise you can’t proceed. That’s the way other servers work.

I'm surprised that playing games with multiple boards on the screen at once has not become a thing. Yet.

One could answer fellows who search for a playing partner are willing to play such a promischess guy!?

It is essential courtesy towards you opponent to play one game at a time only. Playing several games simultaneously is insulting towards the opponents. Lichess should not allow this.
Banning 2 games at a time would do more against people letting their time run out than all the stupid warnings.

It's also possible at
You'll never have any guarantees about the opponents doings and motives.
The offered flexibility here is a nice, even must have, feature. I don't think it avalanches too much.

As long as players aren't violating Lichess' Terms of Service I don't see an issue.

I think Sargon's point might have to do with the fact that some players leave games without resigning, which has caused some issues on the forums.

I suggest that Lichess allows a "Claim Victory" button:
* As soon as a person [in a losing position] starts a second game (really? that's pretty disrespectful); or
* 10 seconds after a person [in a losing position] switches to another tab/window.

you can play multiple games at once ? it gives me a you should resign thing

Allowing multiple, live simultaneous games to be played (besides an advertised Simul) is a mistake by the server, leaving itself open to many forms of abuse. Eventually, lichess will reverse it's policy.
Several "policies" are in place, made by decision makers who have good intentions, but are misguided for a lack of experience in the overall scheme of chess etiquette.