Normal driveways in my area are typically 4" thick asphalt over 6" of concrete
Did you mean 4" of asphalt over 6" of base? There is little reason to place 6" of concrete under an asphalt driveway. The 6" of concrete would support any typical residential loads.
FWIW, I place a few aprons/yr. in front of garages that have existing asphalt driveways. This is due to block foundations located outside of poured garage slabs. As the owners drive over this hollow block space and the asphalt crumbles, holes appear. For garage slabs and those aprons, I will order fiber reinforced redi-mix (5K lbs) and reinforce with cross-tied 1/2" rebar. I don't get any call backs from placing in this manner. IMO, concrete, if placed correctly, is superior to asphalt in most regards.