It's not a false equivalency. Books have been written about it and describe how you defeat REST by doing what you describe.
When you encapsulate most of your operations under POST you basically create your arbitrary protocol. No assumptions can be made about your service. You can make your own assumptions about your own service, but the others can't.
> That would be a fine protocol, and totally REST compatible. What's the problem exactly?
The problem would be that it wouldn't be REST compatible. You should clearly read a few books on the subject. Friendly advice, not a snarky comment.
REST already has idempotent mutating operations, like PUT and DELETE. It's not just GET that's idempotent. So clearly the problem is that you redefine your own protocol, with your own semantics, even though we already have plenty of standardized methods/response codes.
> If there's actually something wrong with that, then lay it out.
You have obviously missed a ton of bibliography on the subject. Before reading random blog posts from random people who have their arbitrary assumptions about what REST is, I'd suggest reading a few books on the subject.
Honestly sorry if I sound snarky, but after 10 years on working with such APIs, and after reading countless books on the subject, it never ceases to amaze me how people still think that GET and POST are enough. But I don't blame you, but the browsers who basically broke the protocol by just using those 2.