There is: your browser or other type of client does not know it can repeat a POST request if it fails, whereas a QUERY request can be freely repeated in case of errors.
Yes. That is what the spec says. However, if the search query is expensive you need some form of caching. Either on the endpoint itself caching the data, or the mechanism with location to redirect to the location of the result.
Putting something in a spec does not automatically make it true. In the real world if you repeat expensive queries more than an undefined amount you get blocked or at least bot-checked.
Why the snark? The existing methods have been around for ages. Many engineers I’ve encountered were not even aware that there was a distinction between “idempotent” and “safe” as attributes of a method and generally conflated them, using “safe” in the sense of the dictionary definition instead of the spec’s.
Elsewhere it was suggested that we can now replace POST with this query. I was trying to be cautionary because just changing the method alone will bring different behaviour. I did so in brevity because I was in a rush. IMHO, that does not call for snark.
Technically a put or a patch is also idempotent. The benefits are idempotent and safe (and semantically appropriate). Post (generally) communicates something is changing whereas a query doesn't
PUT is idempotent, PATCH is not always. The semantics of a PATCH payload are up to the server and standards like JSON Patch (RFC 6902, https://datatracker.ietf.org/doc/html/rfc6902) allow non-idempotent operations like adding an item to a list.
It feels very pointless and there is no drawback of just using POST