Hi!
My immediate reaction is that queries might contain PII (Personally Identifyable Information), and thus would not be shareable. I'm open to other thoughts, of course.
I though about it but I don't see how. Wikidata does not contain any PII and the only thing you can query for is what is in Wikidata. We're talking about SPARQL only, not the full log with IPs, browser fingerprints, etc. of course.