I can't speak for the person who declined these flags, but I don't think I would have been particularly inclined to delete most of them either. A comment of
"+1 good job"
conveys nothing that a simple upvote or Accept wouldn't have already conveyed, but most of the comments you flagged do more than this - they express the commenter's appreciation for a particularly insightful or clever answer. If every question or answer attracted a half dozen people making such comments we'd want to curtail that, but as it is, used as sparingly as such comments are, the occasional congratulatory note for a particularly outstanding question or answer is I think fine to post, and equally fine to retain.
Beyond this, some of these comments are more than bare kudos or thanks.
Something like "Thanks, I added your answer to mine" is an attribution, acknowledging a contribution.
Something like "Thanks, and check out this other thing" points out additional material of interest.
(and note that this comment immediately followed another comment that literally was just a thanks,
which you also flagged and which was upheld by being deleted)
Something like "You just beat me to it, good job!" helps confirm an answer, which is useful to voters.
And finally, even "Excellent work" alone, when said by a puzzle's creator, conveys that the answer is exemplary and fully solves the puzzle as intended, which says more about an answer than a simple checkmark would.
A couple of these were a bit more iffy, and I might have gone either way. But in general I think because PSE doesn't have a huge problem with comment clutter, there's no harm in leaving such comments around, especially when they're sparingly used. (As full disclosure, one of the indicated comments is mine—but I tend to leave very few kudos comments, and that one was well deserved indeed.)
One parting thought....
"There are votes available to show appreciation and even if these comments are still left, they have served their purposes and are no longer required."
I'm actually inclined to think that such comments of appreciation—again, when they appear as infrequently and used as sparingly by their posters as we see on P.SE—are in fact of ongoing utility to the community in that they indicate an answer is particularly good. Someone who comes across that answer in the future may read through it and think "eh, sure, but that's just obvious!" because the explanation looks so effortless it's perhaps easy to lose sight of how hard it was to arrive at that solution, and how much harder still to explain it so well that it makes the tough look trivial. Comments from contemporary would-be solvers who appreciate the answer for what it is, because they were trying to figure the puzzle out themselves and couldn't, point out to future visitors that a particularly noteworthy answer is, indeed, particularly noteworthy. I think there's continuing value in that.