I think the concern is mostly having the comments overwhelmed by "Me too"/"Thank you"/"+1" comments. Appreciation is welcome, swamping interesting content in empty comments less so.
I agree. However, downvoting is not the same as not upvoting. I think it makes sense for "thank you" comments to eventually find their way to the bottom of the comment list because they don't add substantively.
Several times, I've had my "Thanks" post downvoted on threads where the entirety of replies was less than a screenful. IMO courtesy is never a bad thing, particularly when someone takes the time to answer a question you asked. An upvote is (to my knowledge) anonymous.
However, "Me too" is best done with an upvote.
But it also creates a community of enforcers of trivial rules who never contribute anything outside that. Good example of that is mathstackexchange. There are users on there whose sole existence on that site is to remove "thank-you"s from the questions.
The reason that's a problem is because mathstackexchange rewards people for moderating. HN doesn't (as far as I know) reward people for downvoting, so you're not going to get people downvoting thank-yous so they can get more internet points.
If I had had the chance to both win mathstackexchange AND the Internet.. The resultant joy would be so profoundly overwhelming that I would probably have to leave the grid and start a sustainable kale juicing company.