I prefer POST for everything. The main reason why is because HTTP verbs don't match cleanly to every operation. And it leads to a lot of bike shedding around the exceptions. POST for everything, on the other hand, forces you to put the "method" in the request outside of HTTP semantics, which allows you to "just use" whatever verb makes sense rather than trying to map it to the limited ones available.

GET: I want to see stuff.

POST: I want to change stuff.

I don't know how this style cannot match cleanly any architecture.

It's not supposed to be a map to CRUD, it's a bunch of building blocks for manipulating state over a network.