Not entirely. If I MITM your connection to a website that uses a password, I have access until the breach is detected. If I MITM a public/private key log in, I

Not entirely. If I MITM your connection to a website that uses a password, I have access until the breach is detected. If I MITM a public/private key log in, I only have access to the session (which can be made arbitrarily short if logging in is painless/automatic).