I have a feeling that outside Stack Overflow and a few of the other largest sites at many times of day the number of 2k+ users that actively flag and process review queues is quite limited. I have an hypothesis that when an obvious NAA like "Thanks that answer is great!" arrives on a smaller site that the core group of active users at the time:
See it immediately and flag and maybe downvote it.
See it on the first post / late answer queue first and do the same.
Either action removes the possibility of further reviewing it on the low quality queue to recommend deletion which leaves it to 20k users (in short supply on many sites) or moderators to delete it. I have no way to confirm this other than personal observations but such answers seem to mostly end up being handled by moderators while close votes are mostly handled by the community.
I'd like to propose that after raising a NAA / LQ flag you later get the chance to review it on the LQ queue after the normal time has elapsed. That would avoid reducing the pool size of possible reviewers and hopefully get more of them handled faster by the community.