I'm not following how this is different from not even using HTTP verbs. We didn't define them because it's the only possible way to declare client intent. They're cognitively useful for setting expectations, organization, announcing abilities, separation of concerns, etc. The fact that POST is today sometimes used in practice as a safe+idempotent query (i.e. a GET with a body) seems like the black sheep violating those useful qualities.
Client intent is distinct from server interpretation. Distinguishing these is important when defining protocols/interfaces.
A client can blindly PUT a endpoint that does not support PUT, only GET. In the cold connection case where does this fail? The client succeeds at serializing the message, the client succeeds at sending it, the message gets successfully received, and only upon examining the message itself does the server know it should not follow the client intent. This is the same behavior as if the client sent garbled nonsense.
The key here is that it is the server demanding certain message structures. The client is free to send whatever, it just only succeeds if it sends something the server will accept. The server distinguishes, but to the client it is no different from sending any other opaque blob of data. This is thus just a server-constraint, the endpoint is GET-only. To use this website/HTTP interface, the client needs to know that.
It will need to know to format the message correctly, but that derives from knowledge of the documented server interface. If you had just a direct connection with no intermediary participants, then you could trivially swap out HTTP for any other transport protocol without a loss of functionality or behavior. That points to there being no reason to syntactically distinguish on the client to server leg of the transport protocol. However, you still have GET endpoint behavior since that is actually preserved across transport changes, so that is the important class of behavior to define.
The opposing point here is that if you do have intermediarys then they may care about the message format and you may need to syntactically distinguish them. I suspect this is less beneficial than a simpler and more flexible, yet precise transport format.
Basically, we should prefer simple, flexible transport formats and push interpretation (and thus behavior) out to the endpoints which actually have enough context to know the true properties of what they are doing.
