I most recently got hit hard with this in Skyrim. There's a civil war and dragon attacks, but you can just wander off and gather herbs for half a year, and the world pauses and waits for you. I tried playing it straight, as some earnest Nord man genuinely worried about his home being burnt to ashes by war and dragons, but it just didn't work. I felt bad for trying to skip past all that game content. Side-quests stuck to me like burrs. In each place I visited, more sides and guilds appeared for me to join. My character's motivations didn't interact with them, and they seemed curiously unconcerned about the dragons. Soon, I could no longer keep up the pretense that there was any real urgency, any real, living world to interact with.
The problem for me is in the combination of an open world and an overarching plot. I'm fine with something like Dishonoured, which was almost entirely linear. And I greatly enjoyed Sunless Sea, which in a sense is all side-plots, but written in a way that avoids the feeling that the world stops moving when you look away. But more traditional RPGs just don't work. I tried finishing Avernum 2 three times and each time got stuck as soon as the game's plot opened up too many options. I barely got past the intro sequence of Shadowrun Returns.
Clearly I'm in a minority here. Most people adore those Bethesda and Bioware and Spiderweb RPGs, happy to find their niche in some kind of side-plot or side-mechanic like herbs or smithing or decorating your base with lightbulbs. I'm not quite sure why it doesn't work for me. Does my game dev background mean I see the games' inner workings too easily? I like to approach games as things to be won, so perhaps RPGs just don't provide me with the right kind of push-back. Or maybe I'm just spoiled by pen and paper and get itchy when I can't roleplay as freely as I'd like.
If you wanted to combine an open-world game with a central plot, how about picking a coherent reason why the main plot can wait? Pretending there's an urgency that's not borne out by the actual game always eventually undermines things. Instead, have a linear intro section, then open up the world with an explicit "and now you must hone your skills". End the game with a linear section which the player can choose to begin when they're ready.
Or how about actually enforcing time limits? If something's urgent, make dawdling equal failure. If there's some great threat, give the player a countdown. Turn time into a resource: if you have three weeks before the Ancient Evil eats everything, how do you spend your time? The Consuming Shadow does this quite effectively, but it's not an RPG. I am not aware of any game that really combines classic RPG mechanics with time management.
I think it would be fun. You could make something like a computer version of mafia, where you have to figure out who keeps on killing characters before you're bumped off yourself. Or you have been accused of a crime, let out on bail, and have until your court date to find out who framed you. Maybe you are on a ship, and something's been stolen, and you must find the thieves and your belongings before you arrive in port and everyone leaves. Or Big Vinnie's going to break your legs if you don't find the cash by next Tuesday, and you must find the best way to turn time into money.
To me, the ideas listed above sound like tighter and more interesting experiences than your usual RPGs. But perhaps they wouldn't be popular because they turn a single long playthrough into something you play repeatedly until you win? I know some people absolutely refuse to play RPGs twice, because to them, what happens is their canonical version of the story, and repeat plays would cheapen that.
As so often, I feel that this is something best figured out by prototyping, though I'm not sure how to quickly prototype an entire RPG with mechanics and characters and plot and all.