> I see nothing wrong in using same public key to log in from a particular machine to a number of remote machines.

There is nothing really wrong with it; it's a good way to reduce the burden of managing secrets. The downside though is when multiple remote machines need to be contacted because a private key was revoked. Then again, a common need for revocation is a compromise of the machine on which the private key(s) is stored, which can often mean a number of private keys need to be revoked. I think the ideal is still to have unique key pairs for each client-server combination.