Allowing players to destroy needed information is bad design.
Erasable information is an anti-pattern that allows players to lose access to clues they'll need later in the game. Typically the players are unaware they've erased the information until it's too late to recover, or even recall what it may have been.
An example is a blackboard filled with writing that is needed to solve a puzzle. A player could wipe the writing off the blackboard and have no way to recover it. They'll have blocked themselves from being able to solve the later puzzle, usually without realizing until much later.
Aggravating this anti-pattern is when a player is compelled to erase the information. For example, if wiping away the blackboard writing would reveal a pattern they need to solve a different puzzle.
A realistic example of this is placement recall for movable pieces. Imagine a game where you need to collect various toys from around a room, either using them as clues, or placing them elsewhere to solve collection puzzles. Now imagine at the end of this you get a shopping list puzzle that requires you remember where all of the toys originally came from. It's too late, since you've erased that information and there's no way to reconstruct it.
This is an anti-pattern in puzzle design since it permanently blocks the user. There is nothing they can do in-game to get at the information they need. Outside assistance is required.
It's possible to imagine a game where erasable information is one of the key mechanics. For example, you might have a detective game where the cataloging and collecting of evidence is vital to success. In this case, it's the job of the player to take notes and pictures, properly recording as much information as they can.
The players here would be properly instructed about this aspect of the game, being told in advance that information can be destroyed. Given the delicacy of the information, there should be redundancy in the information: destroying a few things is okay, as the remainder are still enough to solve the puzzle.
Furthermore, progress should not be blocked, but the outcome might be changed. Perhaps they don't find the killer, or find the wrong one. As long as the unfavourable outcome is directly linked to the players making too many mistakes, that were avoaidable, and they were forewarned about.
Assume everything in this reference is a working draft, there's prone to be some mistakes and inconsistencies. I figure it's best to publish and get feedback rather than write for years in secret. The terms will change, the structure will shift, and the bugs will be chased out. It'll take a while.