So it's hard to ignore dragons, but the ash storms and the rampaging ash-creatures are easy to ignore?
Yes, because you are never told you can fix it, or told the world is coming to an end. The Tribunal is still fighting Dagoth Ur and they are not even close to having lost (yet).
Having said that, consider the following scenario. Assume that someone knew that in some future, the Great Evil One would try to destroy the world, and that in order to stop the Great Evil One, someone would have to do a number of things. This could be written down in some book, or that person could make up a prophecy. A prophecy sounds more grand, and may give the future Chosen One more support than just being following the recipe in the book. Also, a prophecy may have a greater chance of being remembered than a book has of surviving. So, using prophecies make a lot of sense, even if they are bogus.
Yet we know the Elder scrolls are real, and that the prophecies are real. Anybody in that world would know it.
Why? You write prophetic, but he could have taken too much skooma, for all the player knows. Also ... the player had the nice experience of the Emperors dungeon, so the player could, say, have a beef with the whole Emperor thing. And why should the player care who happens to become the next Emperor? Not to mention that those who participate in the Game of Thrones seem to have a short life expectancy and generally interact with a lot of people who can put you (or your loved ones) to death if you utter the wrong words. Better to go somewhere else.
This isn't ASOIF, anyway you could have a reason to hate the Emperor and everything the Empire stands for, but unless you want Mehrunes to actually win you should still follow his words, and if you want Mehrunes to win then your still screwed because you can't help him.
What is this fascination with being in prison

Tradition.
I think there is a simple flaw in your logic.
If people could truly see the future and write future events down then they would see what you would one day become and this tell about it.
It's hard to say that you can climb to power and not have it prophicized (that a word or at least spelled correctly).
Prophecies aren't perfect, but they can predict a lot. It's then a matter of finding somebody that meets the requirements. Like the dragonborn meeting the requirements for Skyrim, the CoC meeting the requirements that the Emperor knew and the Nerevarine meeting the requirements for Azura her prophecy although nobody believed that last one was relevant because you weren't going to be the Nerevarine anyway.
Simply wittnising the events that transpire while the real hero does all the work?
Sounds like you guys should play Oblivion.
In Oblivion you are still destined to do what you do, just the last part of the final battle isn't up to you. Everything else, setting up the pieces for the final battle was still your doing and because of a vision.
You overestimate simple folks' interest in politics. All my criminal scum knows is that her grandpa also spoke weird things at Uriel's age. For her, it's only logical to grab that lucky opportunity to escape prison and disappear, and delivering the amulet would be very foolish and asking to be captured again or even more trouble than simply ending up in prison. Heck, whomever I give the amulet, most likely will accuse ME for murdering the Emperor and his Blades. It doesn't take an ABNORMALLY dumb, nihilistic and heartless person to care about their hide first - it's just practical. In fact it takes an abnormally noble and reckless person to get involved any further, and why would such a person be in a prison anyway. I generally play good aligned characters in games, only very recently I'm finally trying out something evil or rather simply selfish, and I can tell you that even with a good character it's actually hard to roleplay having to do MQ in Oblivion which is why I haven't even completed it. To a good character, involvement with Septims business logically ends after escorting Martin to Sky Haven Temple, to a bad character - right after speaking to Baurus during tutorial.
It would take an abnormally nihilistic heartless or dumb person to do that in Tamriel. Maybe not if it were to happen here today in the real world, you'd call the one giving the prophecy a nut job and move. That doesn't happen in TES.
Which comes down to the point of not having a dialog option to say no. They're getting impatient with you because as far as they're concerned you said you'd do it, and they expect you to be punctual about it... but there's plenty of reasons a "good" character could turn down the request if the game had simply provided the dialog option.
It's a lot easier to role-play that you did politely turn down their request, unlike Morrowind where it would be completely out of character for Caius to provide you with an easy out.
I'm having a harder time doing that then you obviously. Without the actual dialogue option they are assuming you are going to do that, and I find it harder to ignore without feeling like an [censored] about it.