Will they? Isn't it the same case with email? I used my University email when I was a student. I have a different company email for different jobs? Those that needed to communicate with me because of the job, I would give them my company email. When my work at company X ended, no one expected me to still message me at raphael@x.
The same with addresses from "email providers". They change less often, but it is still possible. My first account was probably at yahoo, but when gmail came up, I migrated, started to tell people my new address and auto forwarded any message that went to the old email.
"Well", that may be a lot of work to some people. To which the answer is "the only way to have absolute stability regarding your identity is if you own it". You can buy a domain a use a managed email service, you can have a domain and have a managed activitypub service provider.
I really don't get people's confusion over federation. It's just like email.
After starting a new job, I don't care about my old job's emails, but my twitter (which is my social network) is still the same
You can. Who said otherwise? Where did you get that idea?
An account at Mastodon (or Pleroma/Misskey/Pixelfed/anything) lets you follow anyone you want. There is no restriction about server talking with each other at the protocol level. If the server is federating and its admin is not trigger-happy with federation, you are good to go.
Wow yeah, this makes a lot of sense. It's too bad nodes became associated with niche hobbies or interests.
E.g. a fraternity/sorority that hosts a node would make perfect sense for a local timeline. I guess the only issue is that these organizations aren't permanent. So people would have to migrate, which isn't a thing for twitter or facebook. I know mastodon has a feature for this specifically but I think people would still find it too confusing if people's handles kept on changing.