Monkeys are just the simiiformes minus the apes. That's just a paraphyly, which is totally fine.

If you don't like paraphyletic labels for aesthetic reasons, just include the apes to make it monophyletic. The main reason we don't is that many people have strong, visceral reactions to being called a monkey.

You can't do that to fish or trees without including a bunch of things that are obviously not trees and fish.