I've wondered what if any advantages attaching the tire this way has over the long-standing two-piece wheel.
Simplicity?
I don't care for this style of wheel, either, but they can be made in one-piece, and still locate positively in the tire. Plus, the builder needn't worry about getting any glue not paint on the tires, since the wheels are finished prior to installation inside the tire...which brings us back to Erik's points. 
Revell has been using these for a few years (maybe a decade plus?) on their Snap Tite kit wheels. I think the '34 Ford coupe might've been one of the first to use them, but the '77 Monte, '57 Bel Air, '63 Vette, and others use the same style wheels.
My thought is they originated in die-cast model kits, as they seem to be easier to assemble in a production setting where a perfect installation on the tires isn't nearly as critical. I want to say the Revell '68 Mustang kits have this style of wheels, too, and the Bullitt and '68 CJ kits were based on a die-cast model. Maybe the same thin with the Vanishing Point '70 Challenger, too?