I've noticed quite a few of these comments being flagged recently. Not flagged as promotion or anything, just a plain "no longer needed" flag after the answer is accepted. Speaking as one mod (I don't know how the others feel about this), I don't mind the extra workload from such comments. The flags are actually very quick and easy to handle: usually I need to click through to the post and get context before handling a flag, but with these ones I can see on the main mod dashboard that the answer is accepted and therefore the comment must be redundant.
Do those comments actually help? Impossible to say, but probably yes. We see so many cases where a hit-and-run story-ID OP posts a comment to confirm the answer and then promptly disappears from the site, never even seeing the comments informing them about the accept button. If there's already a comment to inform them, that must make it more likely that they'll accept before disappearing, even if there's no way we can actually collect data on this.
Does it look like begging for rep? To some people, yes. You've already had an exchange in comments (presumably what sparked this meta post) with another user who said: "it's just spam really, and could be interpreted as manipulating new users to accept your answer just because you ask them to, rather than for the usual reasons to accept an answer." That user was willing to assume good intent in your case, but you'll come across others who aren't.
Restrictions for when you shouldn't do it.
- IMO, it's OK to do this for story-ID questions, provided you emphasise clearly that the OP should only accept if that story is the one they were looking for. We don't want them clicking the accept button just out of gratitude that someone tried to answer even if they got it wrong, maybe thinking it's a different kind of upvote button.
- Story-ID questions are special, because there's always a single correct answer and everything else is just a good try. This is also the only type of question where our duplication policy depends on acceptance. For other types of question, I think the risk of being seen as manipulating rep out of newbies outweighs the benefit of having a correct answer marked. I deleted one of your comments today on a history-of answer.