But visualising moves ahead is a big part of finding the solution! In a real OTB game you can't just say "let me just get out my analysis board".
Analysis board for daily puzzle
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Indeed, but in OTB neither does your opponet refuse a less than perfect move. I'm thinking that the puzzles are intended to help us learn. With the analysis board we can explore various options and may be see the weakness of our proposed solutions. Without an analysis board solving the puzzle can almost become a guessing game. (Guilty, at times.)
How about including access to an analysis board with the daily puzzle? Often, and today's "Cracking the Defense" puzzle would be an example, I would like to explore different lines, and easy access to an analysis board would be a great for that purpose. Then for more difficult puzzles an analysis board would let me look at the various solutions I am considering for a puzzle before I attempt them on the puzzle. It keeps me away from a trial and error approach to finding the solution.