Privacy. If someone owns two servers you're logging into, they can associate your logins if you use the same key. Another case is associating you with your GitHub account (as your ssh keys there are public)

This is fingerprinting across different identities which is a form of discovery. It’s why I have separate ssh keys for work and personal projects in the first place to better avoid associations across different online identities (with the full understanding that if I’m targeted I’m already against attack vectors that require much more sophisticated defenses). Firstly, for work projects I can give up my private key to my employer as I leave and I won’t care because it was only ever used for work and it would be some reassurance to my colleagues that they can at least access the stuff I used to have access to.

If you run a dark net market and your servers are at the risk of being seized, then no, you don’t want stuff like whoami.filippo.io to work.

It all depends on your threat model, I guess.

Assuming you use different keys for different services, the answer would be: privacy.