Even I have trouble picturing a completely static world where nothing happens. All worlds have some level of dynamic activity. There is a level of pacing though, and this can be measured from world to world.
Yet you are advocating a world were nothing happens unless the player characters initiate it.
One thing to examine is out of the ordinary, non 'status quo' events. For example, the crime rate in our world stays relatively the same in any given area from year to year. But sometimes there are crimes that are out of the ordinary, that are so bizarre they capture attention. Examples include a person in a position of power being assassinated or a maniac going on a killing spree or a terrorist bomb being detonated.
These happen every day in the real world and careful studies have shown that's been the case for a long, long time.
In your fantasy world, how often do events like these happen in a given community, like a small town? Once every decade? Every year? Every month? Every day? Every hour?
In the last fantasy game I ran there might be one noteworthy bizarre event a month to a year. Cow with two heads, man bites dog, crop circle, whatever. Most of these have no real effect on the world as a whole. They don't in real life. On the small area the PCs are dealing with they can.
In a more status quo sandbox game, these out of the ordinary events happen much less frequently. Sure there are routine dangers, but nothing so unusual that they would change society.
Danger or the perception of danger changes society by it's very nature.
Another analogy is weather. Status quo does not mean it has to be always sunny (or cloudy) in the world. There are storms and seasons, day and night. Sometimes there are really big storms that wipe out communities, but how often does that happen? Maybe once a generation? Or have you placed your campaign in the magical medieval version of a hurricane prone gulf town, where these things happen every year?
Part of the world I last ran and hope to run again are like that. Others are not. Most of the action last time I ran it took place in a place prone to bad storms because that's where the prizes were to be had.
The DM determines the goals and sets the timeline.
Depends on the table.
More Dynamic: There are doomsday cults hiding in every tavern cellar who try to enact a different wacky scheme to shake up the world every day.
Wow. That's a completely ridiculous extreme. I've only ever seen that in a supers game where it's to be expected.
More Status Quo: There are fewer cults, they gather farther away from society and for they are 'sleepers', willing to wait for years after the campaign starts before striking.
I think you're conflating different things here. Status Quo would involve the cult not doing anything until the PCs stumble on it. Dynamic would involve the GM having some idea of the cult's motivations, methods, progress, and timetable. A cult of the tentacley-faced squid god has a scheme to wake him up they have been working on for over a century. If they can do X, Y, and Z by the next solar elcipse, something bad will happen.
Now, if the players ignore the hooks or just don't see them and go and follow something else, a decent GM will either have them fail quietly off camera or have them succeed (or fail) in some way that has the potential to cause problems (read: adventures). A bad GM will have them under every rock until the players address it. A stunningly bad GM would run to the date of the eclipse, describe the end of the world, and then end the game, blaming the players for not saving the world because they didn't think the rumors of the cult were compelling or didn't even hear them because they didn't stop at the right tavern.
You seem to be saying all dynamic worlds involve world shattering events, all the time. That's not how things go.