I think you are correct. When you run the analysis, it doesn't list Kc1 as a viable move but if you start the analysis after Qd3+, Kc1 is a nearly equal choice.
You are correct when you State that a 1700 problem should be more straightforward.
I don't know the answer to all your questions.
I don't think clicking the "report" button on this puzzle will work because the engine sees Kb2 as the line to analyze.
Perhaps if you write to support, they will pass your questions on to the right person. (I will try to find out who that is too.)
Mods, please move this to the right section if it isn't there.
But during my daily survival chess run I ran across this problem:
https://www.chess.com/puzzles/problem/1209336/practice
After white plays b4, I took a long time to figure out a forced win. Much longer than I did on subsequent puzzles. So I wondered for a while if this was mis-rated. Analysis with chess.com engines afterwards shows the win is there, not so straightforward.
My thought process was: Qd3+ is the best move, but Kc1 takes a good long while to work out. I suppose I could play it and go by the seat of my pants, but I tried to calculate. And I wondered if I was missing a clear forced win, since 1700 puzzles--while not pushovers--usually don't have 6-moves-deep analysis. And while, at the end of analysis (Qe3+, black takes all the pawns) White is busted with an exposed king, the material advantage is two pawns--not overwhelming.
So I was a bit shocked to see Kb2 after Qd3+, since that (or Ka1) was clearly weaker than Kc1, and it quickly leads to a crushing material advantage for Black. So it brought up a couple questions.
1. is there an algorithm for chess.com to determine the next move for white/the losing side? If so, is it purposefully bad on occasion to give you the winningest line, or to give you a break on some puzzles?
2. is this sort of puzzle fair? If it is about tactics training, we want to do more than just say "Well, this move looks like it works, let's play that." Process of elimination is valid, but in this case, the player gets a real gift.
3. how are puzzle ratings calculated, anyway? Is it strictly based on the ratings of people who get them right and wrong, treating each user's try as a game with ELO or Glicko adjustments based on pass/fail (win/loss)? In this case, the obvious first move and bad computer move would seem to skew a technically tricky/deep puzzle into something more average.
It's understandable that some tactical puzzles are better than others. And of course sometimes I'll get puzzles where I don't understand why they're so high/low rated.
But in this case finding a full win was clearly more rigorous than for some puzzles 300+ points higher. So this may just be an outlier that isn't quite odd enough to flag as bad, or one that just didn't mesh with me, or of those puzzles to remind the player "Look, you don't have to calculate everything fully, just use process of elimination." And this doesn't happen very often. It's just, when it does, I'm curious about how these things work.