Many websites actually do this. It significantly weakens the defense against the forwarding problem because people will blindly click submit. But IMO it's an acceptable compromise for anything not business-critical.

Some people have come up with a trick to hide the unsubscribe link with CSS when it is inside a <blockquote> tag, as in a forwarded email. It doesn't work reliably, though. HTML email is still stuck in the 90s, it's impossible to do anything fancy inside of it. Much easier to send the user to a real web page for an actual transaction.