That's based on the premise that the model T was less expensive than a horse
No, it's based on the premise of the Model-T being the cheapest possible automobile.
It's not obvious that the automobile would take off, though the piles of horse feces in city streets should have been a hint. But it is obvious that the best chance anybody has, starting a new market, is to go for the least-expensive possible vehicle.
otherwise Ford wouldn't have been the only one in the USA doing it so cheaply/successfully for the better part of 10 years.
Ford found a way to do it very cheaply, that had escaped all others. There were plenty of other car makers out there, and once they adopted the assembly-line model, they started competing with Ford, too.