Idempotency is an important attribute for correctness. Yep, you can document that POSTing to $ENDPOINT is idempotent, but you can't communicate that to caching layers throughout the network. QUERY, by definition, is idempotent and cacheable.
Great point. I wish more people realized that intuitively.
At least support - or lack thereof - for a new verb is unambiguous (compared to changing the semantics of GET)