I do know Ford Model As had 19" wheels. In one year only, 1932, Fords had 18" wheels. Then 17" for a few years and a 1941 Ford I once owned had 16" wheels. As I remember, most US cars, including Cadillacs, in the late '40s and until the mid-50s had 15" wheels, then 14" wheels beginning in the late 50s.
Cadillac never went to 14" although other GM Divisions did.
As streamlining became a design feature, the wheel/tire assembly had to fit into the enclosed fenders.As horsepower improved, the 'contact patch' had to grow to accommodate traction and braking.As suspensions imroved, the sidewall construction had to change to give a better ride.As for low profile tires, except for some real performance cars, i think it is more form over function as popular tuner cars seek to give the illusion of performance (like having the eye on the back as if it is on the dyno so often that they don't need to take it off, etc) and urban vehicles tend to style more towards 'rollin' on 22s' or whatever the vernacular would be.