This approach is so common in RPGs it's like dwarves with Scottish accents; a better question to ask would be whether there's an RPG that doesn't do it - one that hurries you up instead?

I mean...Dark Souls is the obvious answer, but that's almost a different subgenre of RPG. Dark Souls does have side quests, but they are obscure and often incidental to the main quest. They also skirt this problem by having "time" be a loose concept in the lore - in every game, the world is in the process of slowly ending, in a literal way that fucks up the flow of time.