This whole thing is non sense. It basically mixes technical constraints (body or not body) with a functional requirement that arises from people that are tied to semantics of the protocol.
HTTP is transfer protocol. It should not ever imply anything at the business level.
Yes REST made it's worst mistake out if it by giving a meaning to the verb.
Yes proxies rule how the body is re-interpreted in spite of the will of the sender (wtf).
But the original RFC states clearly that any verb can be used. This is how WebDav normalised its own.
But playing fancy by introducing a change that all HTTP implementation will have to honor is a very bad and irrational choice.
Yes this, yes that, yes the other, because proxies are in agreement with patterns are in agreement with the HTTP spec that methods exist and have semantic and functional requirements. Your 'should' seems to be discussing a hypothetical technology that is not HTTP, because HTTP has worked this way since 1997.