Unable to login to iMessage on Big Sur

[xrosser]

As you reported you have successful connection with a friend's account, that proves there is nothing wrong with your settings as it stands. Without being facetious or condescending, the solution is patience.

I called Apple about this issue (having it on my new hackintosh as well as the one in my bio). iMessage will launch and then quit to the login screen again. Relatively new Apple ID. Of course, I used a real MacBook for the call when asked for my serial, and claimed it was happening on that same MacBook.
I just wanted to get the advisor to check whether there was an account block using their iCloud Support Tool.
After asking questions to nudge her in the right direction, she confirmed my account doesn't have a block/soft ban, so that couldn't be the issue.

So yeah, don't keep fiddling with it, or else you may get a block on your account because of spammy activity. Just be patient and it may resolve itself in a few weeks or so.

 

[ncortines]

Hey, I think I'm on the same boat.
My iServices stopped working as you describe (going back to login without error) after the upgrade to BigSur.
Previously on Catalina had no issues.
I can still use iServices on other apple devices (mbp, iphone).
During a call to apple support they told me there is no ban/block whatsoever (the guy was clueless)
Just be patient and wait? I'm currently on 11.3.1