You make a good point about the "racing against time" feeling. I mean, I could answer you that this would be a problem for the player if he is doing a kind of metagaming knowing that certain events/jobs have a time period (probably that player searched the internet for available events and is trying to complete all of those that interested to him). Tracking the passage of time is a technique to try to make the world change over time and thus seem more organic and real. You could still relax and go fishing, explore, or dedicate yourself to making a thousand knives to improve as a blacksmith... and the world you would experience would adapt to those choices the character made, just as it would happen in a tabletop role-playing game campaign (TTRPG) with a Game Master... well, at least it would get closer.
But of course, an incorrect way to apply it would be something like in TES Daggerfall in which one of the first missions of the main story/campaign is that you have 30 days in the game from the moment you receive a letter to go meet a person in a tavern in a city and they tell you that theperson will only wait for you in that tavern for 30 days, and if you do not meet that person before that time is up you will no longer be able to meet her and therefore you will not be able to continue the series of steps to continue with the main story/campaign. But something like this also happened in TES Morrowing in that you could, for example, kill important/relevant characters for certain missions/events of the main story ahead of time... so then you could no longer complete the main story. In both cases the game let you continue at your leisure in the open world but without being able to follow the main story/campaign. Something like this would be valid... but being the main story of the game, it would be a lot of lost content (although, well, I am one of those who always chooses to end the Dark Brotherhood in Skyrim even knowing that it has a very good story, interesting characters and good loot). In Skyrim, the immortality of key characters for any plot considered relevant is implemented, I don't know if that was already implemented in Oblivion.
And, also, the application of the world/story changing according to a time meter adds a lot of replayability, especially for those who want to see all the possibilities. But programming something like this can get incredibly hard and time consumer because it's a lot more story and variations to write than a frozen world until the player starts the chain of situations/interactions, which is much simpler and straightforward.