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No jumping has appeared in a lot of games. Sometimes it's to limit the player's actions, sometimes it's just because you don't need to. For example, not being able to jump in Bionic Commando is to make you use the grapple and work around this disadvantage. Not being able to jump can make some puzzles more challenging.
No jumping can also limit the player's movement. A row of chairs that you could jump over ? Yet you can't. This is the game making you follow a linear path. Sometimes, no jumping can make a game tedious and frustrating but most games are designed around the idea that you have no jump, so you don't even notice that this ability is missing.
They can jump in some cut-scene or some interaction but not in the whole game.