A jar full of puzzle toys sits on my coworker's desk. One of them is a wooden lattice that falls apart when you twist it just so. The trick is figuring out how to put it back together. Another is a kind of double-jointed Rubick's Cube that can contort itself into shapes other than a cube. He plays with them to relieve stress.
This behavior is almost expected of nerds, but it's still odd. If a waiter spent his off hours conducting pretend tea parties with Piglet and Pooh, you'd probably think it strange. Many people who grapple with hard mental work all day long go out of their way to take on more. Why?
The point of puzzles is that there is an answer, one that follows certain rules. The rules might be hidden, but there is no doubt that they exist and are consistent. A maze with no exit isn't an interesting twist, it's broken, a violation of the contract.
There are few things more frustrating than to be on the trail of a question that may not have an answer. Our instinct is to avoid that feeling as much as possible. You have to force yourself through it.  When your day job is full of uncertainty and dead-ends, kicking back to play with something small and tractable is both a relaxing change and practice.
But there must be more to puzzles than a hidden answer and a set of rules to follow. I think there is an even deeper connection between bounded puzzles and mysterious open problems: they tend to give rise to each other. The playing of puzzles kicks up inconsistencies in the rules, or ways to creatively abuse them. The search to explain those fractures can reveal new realms of puzzles.
Rules imply the possibility of cheating. Pulling the stickers off a Rubick's Cube and rearranging them is certainly cheating, even though it satisfies the stated goal. It's cheating because it refuses to deal with the puzzle on its own terms. There's a whiff of dishonor, like peeking at the answer sheet.
Like other crimes, cheating comes in degrees. Disassembling a Rubick's Cube is more like misdemeanor cheating. By tinkering with an underlying structure you risk learning something new.
And remember the maze with no exit? If you find part of the contract is violated, you are free to violate the rest. You can carry a ball of twine and make your own exit out of the entrance. You can knock down walls, cut the knot, "cheat" by escaping one set of rules and jumping up (or down) a level of reality. There is no guarantee that the new level will turn out to be consistent either. Finding out is part of the new game.
At the other extreme, I think this explains the popularity of LEGO. There is no way to misuse them short of destruction. Every arrangement of LEGO is a valid theorem. The combination of a single level of rules and the large "size" of that level is the essence of its special appeal. In a sense, it's the ultimate puzzle because it holds no mystery.
"Mopping-up operations are what engage most scientists throughout their careers... The scientific enterprise as a whole does from time to time prove useful, open up new territory, display order, and test long-accepted belief. Nevertheless, the individual engaged on a normal research problem is almost never doing any one of these things."
— Thomas Kuhn, The Structures of Scientific Revolutions
 Actual avoidance may be the smart thing to do. More tragic is to convince yourself that there must be an answer, always just around the corner.