You benefit more from having to use your visual skills.
Moving pieces while solving puzzles
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In Yusupov's books, he suggests you try to solve the puzzle without moving the pieces. But if after some period of time you still cannot, then he suggests you start moving the pieces around.
Nov 1, 2018
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#4
Don‘t move the pieces until you‘ve solved it. Then play the solution out on the board
Nov 1, 2018
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#5
pdve wrote:
The one reason why amateurs are never as good as Grandmasters is because their visualization is poorer.
"The one reason?"
Maybe you mean one of the many reasons.
Anyway, if you want to improve something, you have to practice it.
If it's hard to visualize for you, then you need to do more visualization practice, not less practice by letting yourself move pieces, lol.
Nov 1, 2018
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#6
Also, I'm actually not sure that GMs can visualize moves better than I can.
Seriously.
I mean, obviously some have extraordinary skills, like Gareyev, and probably most GMs can do it better than me, but all of them? I somehow doubt it.
A GM isn't going to beat me by seeing 10 moves deep. They're just going to look a few moves ahead... it's just that the moves they look at will be much more pertinent, and their evaluations much more accurate.
Sure a GM can see 10 moves deep if the position requires it... but so can I. It's not a big deal to visualize 10 moves, but it's extremely hard to visualize 10 good moves 
I find chess puzzles far more entertaining if I allow myself to move the pieces. Not only do you get the satisfaction of solving it correctly you are able to clearly see the beauty of the moves. The one reason why amateurs are never as good as Grandmasters is because their visualization is poorer. So when we are training ourselves to recognize patterns better then why hold back due to this handicap. I think it is acceptable(till we become better players) to move the pieces and learn chess this way.