Tactical exercises. Does time influence the score?

I think the same rule that applies to blitz compared to standart goes for puzzles.

I find lots more improvement in my rating if I play many classical games than if I play many blitz games.

I play time puzzles on chess.com and I don't feel I am improving. In fact I have been stuck in 2000-2100 for more than a month.
If I don't see improvement then I assume it's not working, but it's more fun at least.

@MyPunIsTwoWeek
I think you're making the argument for no timer on the puzzles. With a timer I think the blitz comparison is more applicable. As a teenager all I ever did was play blitz. And my play was (and still is) shallow. If I had played more slow games in my youth my understanding of the game would be much better.
Puzzles with no timer gives the opportunity to think more deeply about the position. Taking advantage of that opportunity is of course up to each individual.