The games are like that. Games very often tell you to hurry up or otherwise (put the reason here).
Yeah, which doesn't mean they need to be. Also, please note that "urgency" is just one angle of the topic.
The point is setting stakes and then ignoring them completely. Which makes you wonder why to set them to begin with.
What would be the point of wasting resources creating a lot of side content if the player felt they had to rush the main story otherwise they would lose?
No design that "forces players to skip content" is particularly appealing, but the good news is that you absolutely don't need to do it to have internal coherence.
Setting some limitation only on a specific, maybe even optional sub-goal, is not going to force you to skip half of the game's content. You could also be forgiving with your restrictions.
For instance an example I already mentioned several times is how Kingmaker gives you three months to complete your first main objective... Which is WAY, WAY more than what you need (and in fact you can complete that part of the game under a month for an extra reward and still do 100% of the content up to that point).
In general it's fine to leave time to the player to... well, take his time, as long as you don't keep repeating him how much he needs to run.
You can give the player up to 10x more time than he really needs
Which is fine? The goal isn't to punish the player, but to live up to the stakes you set up and be consistent with them.
but he will still feel that he has to rush, which will probably not make him have too much fun.
Most players really don't like time limits.
Aside for the fact that they can fuck off into Oblvion and I disagree with them... I think you are focusing on "time limits" a bit too much here. The point wasn't "put the player on a tight clock". It's "if you say that something bad will happen, makes it sure it actually happens if we fuck up badly".
Otherwise is just... Condescending game design, I'd say.
Also, fun fact: BG3 already has "time limits" on some quests and optional objective, and their current implementation is even less forgiving than what I'm suggesting.
Here's a list about act 1 from a dataminer:
ong rest while druid grove is initially under attack -> all outsiders die
Long rest and anyone at the grove has died due to goblin raiding parties -> they get buried
Long rest after starting Harpy event -> kid is eaten
Long rest after entering druid grove without killing bugbear assassin -> begins killing refugees
Long rest without resolving the confrontation right after you enter the grove -> autoresolves
Long rest after grunting kid disappears -> reappears
Goblin "warpaint" on -> removed
Goblin priest confronted and not killed -> goblin temple on alert
Poisoning goblins -> goblins are poisoned
something with goblin torturers
hag well water makes you sick after a rest
swamp brothers die after a long rest
shadowheart can only be asked about shar once a day
a lot of party banter after doing things then resting(probably hundreds)
tavern burns down
lots of tadpole stuff
dog goes to camp
act 2 stuff I don't want to spoil for myself so I skipped
any quest that registers for a night update(probably a lot?)
lots of companion stuff...
