I would say that "relevant to what the players want" is the important thing. Not all characters at all times, necessarily, but generally the focus of play is going to be about something that's relevant to one or more characters.
That's because you're using the goals of GP and XP. If that's all that play is about, then sure.
Quite often IME there are but two truly important things to many players: surviving, and getting rich. Anything beyond that is a bonus.
But we're talking about games where that's not the focus. The play is meant to be about more than that.
In theory, perhaps. In practice, unless you've got a high degree of player buy-in, it'll end up being about gold and levels.
Sure, character wealth may be a goal, or my be relevant toward achieving a goal, but there are going to be other goals beyond that.
Completely depends on the players, and I probably run for a more casual lot than you do.
And that to me is so much more contrived than what I'm talking about.
You're annoyed about some potential instances of coincidence. Moments of contrivance. Yet you're perfectly fine with your world revolving around the gaming activities that you want it to.... that killing things and taking their loot is not only viable, but common. A contrived world.
Given as it's a world I made up, and that in its physics, geology, cultures, etc. it has to account for magic (both mortal and not) and divine interference, I find no problem with having it be a place of conflicting goals, cultures, morals, and species.
In other words, I'm going to unapologetically make it playable.
What I'm not going to do is tailor it to any specific characters. Quite the opposite, in fact: I'm going to try and make it such that
any character or group of characters can find something to do there if they look, without regard to who those characters might be at any given time.
What if the characters were not pigeonholed into this idea of "adventurers" in the traditional D&D mold? What if they were something else?
Then the game would have a different focus. If the characters were diplomats, for example, then it'd tend toward the non-violent intrigue/diplomacy game I mentioned earlier. If they were rulers and monarchs it'd be a game about ruling realms a la Birthright. If they were knights it'd be about knightly stuff (and would draw heavily from
A Knight's Tale for its flavour if I had any say in it!).

And so on.
Who says the PCs have to go anywhere? I've had several campaigns that took place in one city.
How long were those campaigns? My experience is that if they stay in one place too long the players get bored of that place, which inevitably means the characters will soon enough start doing things they shouldn't, thus wearing out their welcome. They'll have to move on.
Also, in a long campaign it's fun to change up the background or atmosphere for variety's sake. The world has jungles and deserts and oceans and arctic and forests and cities and dungeons - might as well use all of them as adventure backdrops at some point, hm?
Who says that where they may be is the only hotbed of adventuring? Why would that be the case?
Those GMs who see the PCs as the world's only adventurers would have it this way by default.
So why not work with the players (especially in a one on one game) to come up with goals, and then instead of running a randomly selected module, craft adventures that relate specifically to the characters they've made?
Because we both thought it'd be fun to run something chosen randomly. Hell, all the characters were random-rolled as well, even down to class and species. Odd thing happened, though: that party somehow ended up working out really well and are still going three real-world years later.
Do you think that anyone is actually suggesting this?
That the Emperor should conveniently show up shortly after the players decide on a whim to overthrow him?
Yes, I get the sense that some here
are suggesting exactly this; that because the players have decided their goal is to take out the Emperor, it's now my duty as GM to - by way of focusing on their stated goals - somehow put the Emperor in their path.