Think about it. When your client makes a GET request to an URI X, what it's saying to the server is: "I want a representation of the resource located at X, and this operation shouldn't change anything on the server." A PUT request is saying: "I want you to replace whatever is the resource located at X with the new entity I'm giving you on the body of this request". A DELETE request is saying: "I want you to delete whatever is the resource located at X". A PATCH is saying "I'm giving you this diff, and you should try to apply it to the resource at X and tell me if it succeeds." But a POST is saying: "I'm sending you this data subordinated to the resource at X, and we have a previous agreement on what you should do with it."
If you don't have it documented somewhere that the resource expects a POST and does something with it, it doesn't make sense to send a POST to it expecting it to act like a GET.
REST relies on the standardized behavior of the underlying protocol, and POST is precisely the method used for an action that isn't standardized. The result of a GET, PUT and DELETE requests are clearly defined in the standard, but POST isn't. The result of a POST is subordinated to the server, so if it's not documented that you can use POST to do something, you have to assume that you can't.