I don't see it that way. Bethesda introduces you into their game with some sort of urgency, like you have to deal with Dragons problem in Skyrim or find Shaun in Fallout 4 ASAP, yet they also dangling shiny things in front of your face which distract you from their initial hook. Meanwhile, New Vegas gave you some clue about this guy who shot you and you would consider whatever it is you were delivering might be some important item, yet along the intended way to the Strip you got to meet these people in the Wasteland, including the NCR and the Legion, and on the Strip you might consider that Benny and the Chip might not be that important for you after all, so there's really no sense of urgency at all.
Fallout 1's narrative hook is that it's still relatively early in the timeline, being closer to the time of Great War, so resources like food and water is absolutely important. Despite being the first game in the series, I'd say it's THE best implementation of time-limit in the series, if not among ALL videogames. Coupled with smaller but solid scope, it allows much better focus for the game.
Besides, having finished the game multiple times, do you think there's anything important in the game you wanted badly, of which the time-limit hinders you from getting it earlier? I'm thinking power armor, but if it's your first time just following the direction actually works better to get the feel of the game.