It's definitely not a "tremendous" amount of work. At the bare minimum, you copy your POST code and change the verb, that's it. There's no need to cache, so you actually can handle it basically as idempotent POST.

> You can just handle your POST request idempotently

You actually can't though, and you don't usually have to look far to run into a case where this gives the wrong behavior. Better to just have a separate verb.