Of course, it goes without saying that this can only work when the puzzle is randomly generated (say, something like minesweeper/bejeweled) and not hand-designed levels (such as trainyard, theseus & the minotaur etc).
I am currently thinking that this can instill a sense of urgency to the player and make them feel more challenged. Along with increasing the actual puzzle difficulty, a time restriction could be another way to increase difficulty, and the combination of both can be used as a way to give a sense of progress.
Also possibly, incremental time increases when solving parts of the puzzle (like time extensions in racing games) could be used for these games.
What I'm wondering about is, what's the accepted thought about using time limits? Would they work as I'm currently thinking or am I missing anything?