It's not their "mission" but it is their system. If you have a static IP address where "...the address migrated around the world with you..." how do you think that will work for people that _NEED_ anonymity?
The title of the article from Tailscale is "...to fix the Internet"... if it was "only" about "your own devices" then you are assuming they are thinking small.
You're assuming that they're thinking something completely outside of anything they've ever said, and something that nobody actually wants. Your assumption is the one that's out of left field, not mine.
I don't have to prove you wrong, I'm not making an assertion. It's on you to prove that your assertion is correct, and you have nothing more than your opinion backing you up.
The idea of "you have something permanently static that identifies what is yours" on the internet that never goes away, and it runs through a corporation's server, that supposedly is marketed as "fixing the internet"... do you really think this sounds good?