This site has had problems with low quality posts getting upvotes on the past, with some of that due to the HNQ (and I’ve seen this happen recently too). This proposal should theoretically reduce the number of low quality posts getting upvoted, because people with some interaction with the site, or have read the meta post about not upvoting bad posts will be less likely to upvote bad posts.
Note: Similar requests asking for upvoting to require gaining reputation on the site (which I’m fairly certain was posted by a high rep user of politics SE) have been posted before on the main meta.
Note 2: I didn’t include downvoting in this suggestion because it already requires gaining some rep on the site.
Note 3: This was originally about the tour instead of that meta post, but Philipp’s answer made a good point that that wouldn’t work, so I’ve changed it to something more relevant