Sure it's possible to: have a strong password, use it only for a single machine, keep it in a good password safe, never reuse it anywhere, have the discipline to not make it short/easy to type/easy to remember, change it every time a server is compromised, etc....
Or you could get all that for free with public keys. Yes a private key is like a very long password, but the important part is that it never leaves the client side and it's safe to use on every computer you want access to without the hassle of remembering one password per server.
If you access many machines, how will you know when one is compromised? How will you prevent an attacker from logging in as you?
Public keys really are the better way to handle user auth, less of a minefield for regular users.