If we're going to play the "should" game, whatever originated the body "shouldn't" have because the spec says that's illegal.

Although we could also go with, a proxy shouldn't delete the body, it "should" reject the request outright as ill-formed.

The meta-point I'm making here, which I'm sure will be missed if I don't spell it out, is that if we're going to talk about what "should" be done when it is explicily out of the scope of a standard, there's no way around the fact that there are multiple completely sensible ways to extend the standard and there's every reason to expect that in the real world people aren't going to agree. Sometimes they manage to, but even then often quite imperfectly. Our human intuitions that standards are something that are "built" is perhaps not wrong, but you can also productively look at standards as taking the raw material of all possible things two systems could send to each other and removing possibilities. If you reach into a space that has been explicitly removed, you can't expect everyone else to do so in exactly the same way you will.

                                   A message-body MUST NOT be included in
    a request if the specification of the request method (section 5.1.1)
    does not allow sending an entity-body in requests. A server SHOULD
    read and forward a message-body on any request; if the request method
    does not include defined semantics for an entity-body, then the
    message-body SHOULD be ignored when handling the request.

The HTTP standard does not define a body for GET requests. Therefore, proxy implementations will typically only copy the data from the request header when sending it off to its next destination. They don’t technically “delete” anything. This saves compute (and possibly bandwidth, if the request happened to have a body, although the whole point is that one can safely assume a GET request does not have a body per the standard).