While I love the proposal (apart from the name, I can see the SEARCH verb being used for something that's not search), they should also address the URL share-ablity aspect.
Something like " rel="nofollow">https://google.com/search where query can be arbitrarily large (>2000 URL length restriction) and the browser is smart enough to treat only https://google.com/search as the URL and anything after that as the body. The complete "URL" can be big and shared anywhere else.