So I hope I don't make a fool out of myself, because I didn't verify whether my solution is even correct, but I want to give my 5 cents here, though this is only very anecdotal, as I consider myself neither a good nor an experienced player, but I did manage to solve this puzzle (I guess).
Rc7 jumped to my head as a candidate move right away for some reason. Probably because the puzzle was introduced as leading to mate and then I start with the most forcing move.
After this, Kd8 is forced.
The next step was trickier. Somehow I feel an inner resistance, moving the same piece twice in such small steps, so R4xd7 felt more natural. But there after following the possible responses, I realized quickly, that the Queen protects any threats from my rooks.
So how about Rcxd7? Ke8 leads to Nc7# which is good, but what about Kc8 again? This looked odd, because, what had changed since the last time the king was there? Won't I just be repeating moves if I go Rc7 again? But then it dawned on me, that there is no pawn anymore and the King can't move, so it's check mate.
So to answer the question, on my side there were two mental obstacles that I had to overcome:
- Moving pieces multiple times in very small steps. Normally this feels wrong to me so I was hesitant here and about to disregard that move.
- Not envisioning the board as it will look like after some captures. This missing pawn made a huge difference but there was still the initial picture of the board in my mind.
- (Not fully appreciating the power of the knight to jump around like crazy sometimes, and then covering spots that seemed impossible, but that is a bit off here I would say)