(while I think this isn't the affordability driver) this point about prices isn't really true - compare the graphs of two markets: one with a horizontal demand curve (perfect competition) and one with a downward-sloping demand curve (monopoly) - the first will have no deadweight loss, the second will have substantial deadweight loss.

Markets tend to the second and need state intervention in order to prevent the proliferation of monopolies. Functionally this is intervention every time price coordination happens, which... is pretty clearly what AirBNB is doing!