No, rather than the body being silently ignored in the caching (or even proxying!) logic of some middleboxes, because "since GET will never have a body, for efficiency, we won't bother to check for one."
Yet, given enough demand, and a explicit recommending nod from the spec, these will comply. It's not really as big as problem as everyone seems to think. And it's literally the same amount of work of adding a new verb.
Things might've changed since then, but back in 2009 it was Chromium who disabled bzip2 compression after some ISPs were borking bzip2-compressed pages[1] (although it's mot entirely clear if it was indeed the reason for dropping bzip2), not the other way around. Later in 2016 this was mentioned as being the reason for limiting brotli compression to HTTPS only[2].