It's a little bit more complicated than just sending a hash of the password, but there are ways to authenticate using hashed passwords without sending the password over the wire, for example https://en.wikipedia.org/wiki/Digest_access_authentication or https://en.wikipedia.org/wiki/Password-authenticated_key_agr...

Even so, these protocols require the server to know your actual password, not just a hash of the password, even though the password itself never traverses the network. So a compromised server can still lead to a compromised credential, and unless you use different passwords for every server, we're back to the same problem.