Puzzles, what are they good for?

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Those are cleverly designed, but too hard for me (I don't want to exit the game every 10 minutes to check the answer). Penumbra puzzles are just perfect IMO

Silent Hill puzzles are also too hard for me, but I enjoy it.
I like hard puzzles, that challenge my brain.

Penumbra puzzles are good. But Amnesia is too easy in 80% of all puzzles.

The problem is when the puzzles make no logical sense in the game. When I come across a puzzle in Penumbra/Amnesia, for example turning on the generator near the beginning of Overture, you have a logical reason to do it. Even if you didn't know what you needed the power for specifically (you would most likely find out when getting the fuse), you know what solving the puzzle accomplishes and why you need to do it.

In Silent Hill, when I come across a weird piano with bloodstains on the keys and the game transparently tells me to solve the puzzle, I just get frustrated, plus the school is pretty freaking scary so it didn't take much motivation to take a break, which unfortunately turned out to be indefinite.