More so than limiting the depth of search, the "level" knob in Stockfish makes it select suboptimal moves with some probability.
Hehe, that's an interesting approach! Presumably because even at its lamest setting it still has too much of an advantage.
My assumption would be that it's because it wouldn't make for a great game, it would be "quite good generally, with some huge obvious blunders here and there", but I don't know for sure.
The Stockfish software from TFA is a very far removed descendant from those early dedicated chess computers and usually you can set the level of your opponent by limiting the depth of search to a certain number of ply. That alone is a powerful switch to control how well it plays.