IMO, an ssh public key is not a password and shouldn't need to be treated as such. The public key portion is
public. When you generate an ssh key pair, its like making both a lock and a key, then giving the lock to a server and saying "use this lock on my door". This lock can only be opened with your key, and can only be picked when your encryption algo of choice (ed25519 for me) gets obsoleted.
Sprinkle in a passphrase and now you have good MFA: something you know (the passphrase) and something you have (the private key).
Personally, I don't see a problem with re-using a key pair across multiple servers. I like to do one key pair per client device. This lets you manage server access per device. You can single out and remove just the key from a lost or compromised device without affecting the others.
OTOH, one key pair for all devices fails at this, plus you also have to worry about protecting the private key during distribution to multiple devices. A private key is best left on the client that generated it. Of course, once you hit enterprise, all this goes out the window. As they will probably have systems in place and compliance rules to follow.