All sorts of stuff can be used for agregate, but not all of it produces concerte of the same quality. Also, the problem is local availability... most of the sheer mass of our construction projects is the aggregate for the concrete, so getting the aggregate from a distant source would be almost like constructing the whole building there and then transporting it to its final location!
There is essentially an endless supply of aggregate on this planet, it's the transportation costs that are prohibitive (both in terms of money and of course the environmental costs of transportation).
Not really, desert sand and riverbed sand have different characteristics with regards to smoothness and grain size, etc.. You really can just use desert sand.
I elsewhere read much concrete is made with rare, far away, environmentally damaging illegally dredged riverbed sand, because desert sand (or other more available less environmentally precious substitutes) were unsuitable.