I log into my XBOX account, start ESO and also see the message about choosing my profile. I've just ignored the message and gone straight into the game with no problem.
Yes, this has been happening regularly for me, as well. Only since the next gen update. I used to forget who I was, but now this problem has gone away, thanks to the frequent need to remember.
Honestly, I never identified it as a problem. I just assumed that something on the XBox logged me out of my game account.