This has a variety of uses, but a general mechanism that allows submitting a Quarry resultset onto a wiki page seems it would be useful for a lot of cases.
So for the query, the user can provide a page name on a target wiki that should be updated with the results, and Quarry will re-run query and update it accordingly. They can pick out of a variety of formats, from JSON to Wikitable, etc.
IIUC, the missing parts to complete this task, are increasing Quarry's OAuth permission request in order to allow onwiki editing, and then providing a way to assign a specific wiki+wikipage that should be replaced with the current output of the query (in a specified format), plus a button to trigger that update.
(This would potentially make a lot of the work currently done by bots in pages like https://en.wikipedia.org/wiki/Wikipedia:Database_reports and https://www.wikidata.org/wiki/Wikidata:Database_reports (etc) a bit easier or more sharable (e.g. when a bot stops working for unknown reasons). At least for the non-scheduled reports - the "daily/weekly updates" ones would take more work.)
See also, semi-related request at T74874: Provide a way to add hyperlink in Quarry results/output, which might reduce some of the need for onwiki replication - If the output had clickable links, that's all many people need.
However, the main additional benefits to storing it onwiki are (a) watchlists, (b) transclusion elsewhere, (c) historical data; so this feature would still be immensely helpful.
Since last year, enwiki has a bot for this: https://en.wikipedia.org/wiki/Template:Database_report (it doesn't interact with Quarry - the bot runs the query directly on toolforge and dumps the results onwiki).