From a usability perspective, it's probably because dealing with keys that can't just be memorized is hard for most people.
"The site is asking you to sign up. What secure login key would you like to use?
* Personal
* Office
* Contracting"
You are person 'A' and you have the private key (and maybe password used to unlock the key) to prove this fact.
You don't need different private keys for each and the remote end just has a public key that says the account belongs to person 'A' and that key is public.
The only usage case would be if someone wanted multiple accounts at the same site, and that would be rare indeed.
The only other real concern, site hacks/collaboration leaking where you're a member of by public key, wouldn't be alleviated by merely a handful of keys anyways: you'd need unique keypairs for each to be truly secure.
But yes, having small memorizable passwords is much more convenient.