> unless I'm missing something I don't think a QUERY verb will change all that much here?

The semantics are important. GET APIs are expected to be safe, idempotent, and cache-friendly. When you are unable to use GET for technical reasons and move to POST, suddenly none of the infrastructure (like routers, gateways, or generic http libs) can make these assumptions about your API. For example, many tools will not attempt to put retry logic around POST calls, because they cannot be sure that retrying is safe.

Having the QUERY verb allows us to overcome the technical limitations of GET without having to drop the safety expectations.

I like the safety aspect of QUERY. Having CDNs cache based off the semantics of the content might be a hard ask. I wonder if this might lead to a standards based query language being designed and a push for CDNs to support it. Otherwise you probably need to implement your own edge processing of the request and cache handling for any content type you care to handle.