The human race is going to keep consuming resources - exponentially more resources, I might add. Thus, there will always be a reason to keep exploiting the resources of our solar system.
That being said, mining something that's closer over something that's very far away only makes sense if you can do so cheaply.
The problem with mining the orbital belts is that it's Dangerous, Fuel Intensive, and attracts hippies.
You've got big rocks spinning around in a circle, smashing into other rocks, breaking into pieces, then smashing into more rocks, to make more pieces which ... I think you get the idea.
2. Fuel Intensive
You're gonna need a lot of very tough ships to start wrangling those meteors out of the orbital rings - we've established that. However, you have to consider that once retrieved (a fuel intensive maneuver in and of itself) the rocks must now be taken somewhere for processing.
You might have a giant refinery parked close by, which is great! But you had to move into place, and now you have to expend fuel to keep it there.
If not, then you're wasting a lot of power/fuel carting those rocks some far away place for processing, which is a deal breaker for any profit oriented business - after all, what percentage of their mass is useful to you? 5% is probably generous.
No, my friend. No one is going to be investing into your orbital ring mining business any time soon. They aren't interested in that bridge you're selling either.
3. Space Hippies
Yo, dude. Those orbital rings have been around for millenia before you came along and started exploiting them for your own gain! Boycott the evil company! Sabotage their mining drones! Beat up their employees! Save the rings! SAVE THE UNIVERSE!
No one likes space hippies.
Mining orbital rings would either come about as a result of a civilization being absolutely desperate for a certain - very rare - resource, or simply because they lack the capabilities to mine the larger, more resource rich asteroids drifting through our solar system.
Maybe a bunch of meteors rich in a very rare, alien alloy crashed into planet X at a certain point in time. Many of the smaller fragments are now caught in the planet's orbital ring system. If the allow is that valuable an industry might develop around surveying the rings and trying to find as much of it as possible (think Gold Rush style prospecting, etc.).
bonus points to anyone who read #3 in a "hippie voice"