A lot of adventures do if you really look at them. Stop the cultists...before they open the portal of ultimate evil. Explore this ruin...before it floods completely.
True. I said about half of them have time limits. The other half don't. I don't want to be restricted to the ones that do.
Even when I run the ones that HAVE time limits...I often hate when the PCs go past them. It just isn't fun to have to change the plans for my next adventure because the PCs decided that resting was more important than the objective.
I once played in a game where the DM ran one adventure where we had to save the princess from some people attacking the castle. It was obvious that we were delaying much longer than he expected. The princess should have died, given how long we took to get there....but, the DM had planned for the next adventure to be us escaping the castle with the princess, and as the last surviving member of the royal family, using her as a plot device ot raise an army and take back the kingdom.
So, it didn't matter how long we took, because the time limit was artificial. Actually having the time limit matter would have ruined all the DMs hard work(and trust me, this DM wrote 30 or 40 pages of notes on stuff that was going to happen).
When I run a game where the time limit is "Stop cultists from summoning the most powerful god in existence who will wipe out all life on the planet", I don't ever plan on actually implementing the time limit...it's just there to try to give some urgency to the adventure. When will they successfully summon their god? About 5 minutes after the PCs stop them from doing so.
Is is possible to keep running this game after the god wipes out the planet? Sure, you can come up with an excuse as to why he can't do it right away and can be reimprisoned before he regains his strength or shield one city from destruction and run a campaign about stopping him. But, I didn't really want to run either of those campaigns. I wanted to run the dungeon crawl where the PCs attempt to stop the cultists. So, I'll make sure I DON'T have to run those other campaigns by never implementing that time limit.
Players figure this out pretty quickly. When I ran that campaign against the cultists, they'd rest after nearly every encounter and I'd have to say, out of character, "You guys do remember that these cultists ARE trying to summon a god who will destroy the world, right? So, you guys are going to risk it by resting while you still have hitpoints left?"
And they'd say "Well, we don't know how long this ritual could take, right? It could be tomorrow, it could be next year depending on how far along they are in the ritual and whether they have all of the resources required. So, we're out of spells, we may have hitpoints left, but it's possible someone might die next encounter if we have to use only our 1st and 2nd level spells...so, we're just going to have to risk it." (because "only having 1st and 2nd level spells is the same as being "out of spells" in their mind)
Sometimes, you can win narratively, evn if you fail in your objective. Indiana Jones did not keep the Nazis from getting possession of the Ark of the Covenant, but he "won" because the Ark didn't behave the way the Nazis thought it would.
Also true, but it feels lackluster to have the PCs win despite failing. Plus, it just trains them that time limits don't exist. After all, if they can fail to get the Ark, but have the Ark kill all the Nazis...well, guess they didn't need to stop the Nazis from getting it in the first place.
But, see above why actually implementing time limits is often just as bad. It always comes down to the fact that time limits solve nothing.