@hilarybaumann That's always been the case. I get what you're aiming at. For your own domain you usually have to do a bit more effort. In this case it'd be hosting an instance yourself.
But, like I said, there are services which can make your life easier. There are paid services specialized in hosting mastodon instances for you, and you just apply your own domain to it. :)
For most people it doesn't really matter to have their own domain, so long it's convenient for them. I've lost access to servers before and I just moved on to another one. People'll know me anyway, don't care too much about post history.
But you have all the freedom to do so. :)