Considering the body of the text, your title is misleading. And I wish I had that picture of The Dude saying "That's just like, your opinion, man." Because that's what this boils down to. Yet another person trying to justify personal preference as objective fact. More accurate: "The reason I don't like open world gaming(Because I like urgent gogogogogo storytelling)"
As to your question, there are some open world games with time limits, but if you don't like that, I guess you can deal with it.
Open world games are enjoyable to some, and less to others, and if you're not finding them enjoyable: There's the metaphorical door. I hope it metaphorically hits you on the metaphorical way out.
Open world games tend to lose urgency. So what? Urgency only matters to plots which require urgency. Urgency is a crutch. Look at the campaigns of modern shooters. They've got faster and faster, more and more urgent, location hopping and running, never stopping to think. Piling hostage upon kidnapped VIP, upon Nuclear threat, upon butchered friend. That urgency is a crutch for poor writing. Raising the stakes mindlessly to maintain forward momentum.
Open world games work better when trying to set up an epic. Assassin's Creed, Skyrim, the Fallout series, tend to do this well. Rather than needing to run somewhere, you just need to do things. In fact, urgency in writing will also cost you player agency: you're inevitably being told to go here, do this etc. Which doesn't exactly do much for the "Main" character of a story.
Dead Rising is an interesting example (Referring specifically to the second, I haven't gotten to the first. Same principle). Of how not to do things. The urgency added by the ticking clock forces the player to complete the story, but the game also tries to play itself off as something fun, with inventive ways to kill zombies. So the player is split between fun gameplay, and the story. Which isn't a great place to be in, really. The game works better as the sandbox mode, or campaign, because for the story, you're managing several timers: Different groups of survivors, the stupid storyline, zombrex timers. Which is interesting in itself, but never really exploited. Rarely are you in possession of enough information to be forced to make difficult choices (You really have to have prior experience at the mission to know how long it takes to be able to make those decisions. So you either rescue everyone, or lose the game, you don't choose between groups of survivors deliberately, all that often), you just rescue pretty much everyone, and wait by the misssion objectives. The zombie slaughter with the custom weaponry typically takes place in sandbox mode, which does let the player have fun with the mechanics.
So the addition of timer centric stuff actively detracts from the fun of the sandbox. You get one or the other, and to me, the urgency or choices in a linear setting don't do as much for me as freedom.
Sandboxes make good exploration games, and make games more open, and generally more enjoyable, and allow greater amounts of content. If you like more linear progressions, that's fine, but I'm always going to prefer a good sandbox.
