That exists for a reason, and it's not nefarious at all.
Lot of people, especially of the older generation, forward all sorts of emails to their friends and family every day. If one person who received a forwarded email doesn't like it and clicks the unsubscribe link, the original recipient (who clearly likes the email enough to forward it around) gets unsubscribed. That's a bug. If you don't like the unfunny newsletter your uncle keeps forwarding you, that's a problem between you and your uncle, not between your uncle and his newsletter!
The email submission form exists to ensure that the person unsubscribing is the person who is actually on the mailing list. It will not prevent an annoyed nephew from deliberately unsubscribing the original recipient, but it will prevent most cases of mistake by third parties.
Similarly, many unsubscribe links require two clicks instead of one, because some email services used to automatically check out every link they found in the body of an email. A one-click link would unsubscribe everyone before they even saw the email. Nowadays we have better protocols and better email scanners, but old industry habits die hard.