I found it speeded up game play. They had to get everything done before a long rest or start over. Move to another dungeon because the objective left. They didn’t want that to happen so they had to be more careful and get through the encounters without expending resources or bypass through stealth an encounter if they could.
Again, that doesn't sound like speeding up
game play. It's accelerating
the progress of the adventure narrative. Like no matter what happens next, the PCs will always move to "the next dungeon". It doesn't matter to
game play if the big bad at the end of the next dungeon is the guy who got away from the last dungeon, or if he's the boss of the guy who was defeated at the end of the last dungeon. It might make your players less satisfied or more frustrated if they're often unable to progress the narrative... but, again, that's not because game play had to stop. It's because the narrative changed.
An example of rules actually slowing down the game is like 1e psionic combat where 10 rounds of psionic combat take place for every 1 round of normal combat. Every round of combat for the non-psionic characters, you have to stop and do 10 rounds of combat with the psionic characters. For non-psionics, the game
literally stops while you resolve this other thing.
An example of rest mechanics slowing down the game would be if the DM said that PCs recover 8 free HD worth of hit points instead of recovering all hit points at the end of a long rest. Firstly, this is virtually the same as recovering 100% of your hit points for most of the game, and secondly, it involves a lot of dice rolling that doesn't actually accomplish much in the game. It's a bad rule because it makes the table waste time with dice rolling on events that aren't interesting.