I'm with
@prabe on this point. How do you get better at solving mysteries when your deductive skills are better than the DM's ability to make sure that the evidence points most strongly towards their intended solution?
As a DM who runs improv-heavy sandboxes, I encounter this issue a lot. I've been in situations where I'm running murder mysteries off the cuff, and leaving clues before I've even had a chance to decide how they all fit together.
Usually I come up with the best solution before my players do, but sometimes they see an implication of a clue that I missed, so I run with that instead. Their ability to be skilled sleuths absolutely still matters, because the "correct" solution is going to be the one that best fits the evidence (regardless of whether I came up with it first or the players found it before I came up with it).
If skilled play is your focus, I don't see how the DM always sticking with the pre-planned option furthers your goal, unless the pre-planned option is
always the one best-supported by the evidence. I know I can't guarantee that condition will be met as a DM, even when I'm not improvising.