I already mentioned magnets, and while Copper is not abundant, it is not rare either. Since Rare Earth Magnets and Copper are both rather inexpensive, and readily available, I still see the "rare and valuable resources" comment as inaccurate.
The reduction in weight. There is a thing called "flux magnetic saturation". That is the thing that limits size reduction of motors. Axial or radial do not affect flux magnetic saturation. The BMWI3 motor comparison is apples and oranges comparison. Lot of the extra weight in the BMWI3 motor comes from the cooling system. Most of the comparisons in the article come from comparing the radial motor to motors with gearboxes. To me the whole article reads like advertisement.
Although most of my electric motor expertise lies in the larger industrial motors. I know enough about the little siblings to state that the differences in power are mostly from the shape of the motor. Short and fat instead of long and thin. One is not necessarily better, just different power characteristics.
There are 2 large drawbacks in the radial flux motors that are not mentioned in the article. Double air gap and since they don't use stacked shims, they get larger magnetic eddy currents.
The layout of the radial flux motor is not without merits and better and lighter motors would benefit all. The future will tell.