I think that's fine. I didn't really like Skyrim in that us could go 100% in everything and be able to reach the highest podiums in all organizations. If in Skyrim something like a calendar were applied and a time account was followed, especially if the world was not to scale and therefore the time of travel from one place to another was relevant, it would not be possible to do everything in the world with the same character. I think there is value and realism in having to put yourself in the shoes of several very different people who lead different lives, if you want to explore everything that a world in a given space of time can offer. It can feel limiting if you're used to chasing completeness in everything, like something mechanical, but if you want something immersive limitations can be a good thing. In addition, obstacles and limitations can invite ingenuity to deal with them and interesting things, instead of always limiting yourself to always making a character "only optimized in practical things".
I honestly think a global time limit for an open world RPG (or really any RPG in general) seems like an absolutely awful idea, unless the game is either completely built around this gimmick like Majoras Mask, or it's something absolutely crucial to the main story like the water running out in Vault 13 in Fallout 1.
Basically, this would mean that you would be forced to speedrun everything in the game as fast as possible. Gone would be the days of roleplaying actions like sitting at the campfire, visiting an inn and getting a drink, hunting some animals in the forest and getting a nice steak or decorating your base with the spoils of your adventure, as you have to constantly rush from quest to quest, trying to beat them as fast as possible, with little to no moments for careful exploration, or you would lose out on them.
A much better way to prevent the player from joining every faction with the same character would be to lock the player out of the enemy factions if they join an faction. For example, if the thiefs guild would have a problem with the fighters guild in universe, joining the thiefs guild would lock you out of the fighters guild and vice versa because they will see you as an enemy. That way you could limit players from joining every faction without having to apply a global time limit. That way, you could also design quests where the different factions interact with each other like for example having you destroy the thiefs guild if you join the fighters guild.
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.