What does tactics puzzle really train?
I think part of chess.com's tactics problem is that it only shows your the tactics position. It is like a chess book and not taking advantage of the new format.
It would be more useful to be able to re-play the stpes that lead to the tactics position (or even just the last few moves before the tactics position). This way, I wouldn't miss (for example) that I have a queen sitting on the board edge subjected to some kind of attack.
Tactics patterns!
As I've mentioned in many comments, after you do a problem - successfully or not - think about what tactics were used - there are TAGs that indicate what other players thought were the tactics here and at chesstempo.com, and then ask yourself why it took you so long to see or didn't see the tactics pattern. You should know all the interactive tactics patterns on these pages:
https://www.chess.com/article/view/chess-tactics--definitions-and-examples
https://chesstempo.com/tactical-motifs.html
Do they really train your ability to solve positions or do they just force you to remember positions?
one thing I have noticed about top players on stream when they want to remember something, they look up in the ceiling or something, It's strange because I've seen naka done it, I've seen Fiona done it.
To me, it seems more like they're trying to recall a position from mind instead of thinking about how to solve a position.
Like they're played the positions so many times they have all these patterns stored in the memory, I theorize that they are simply recalling them back to mind kind of like taking a college exam when you're trying to recall an answer to write down on the exam.