The main sand used for glass is quartz sand. I don't know if desert sand can be used.
Through quartz sand is still widely available.
The reason we recycle glass bottles is that it's much more energy efficient to create new glass from recycled glass and it's not to hard to sort/separate glass so recycling glass makes sense for reasons which are unrelated to how "rare" the resource it's made from is.
Note that this is only true for glass bottles (or similar), things like window glass is made from different sand mixes and should not be placed into the glass recycling bin at all.
I have no idea if you can recycle window glass (as e.g. non window glass) or similar. But it's not part of the glass bottle recycling process and is seen as a form of contamination if placed in to large amounts in the recycling glass. (as far as I remember)
