My theory on how hot dogs got so popular:
Americans love picnics.
Picnics attract children like they attract ants (great quantities).
Adults pay for the event.
Hot dogs are cheap, plentiful, easy to cook, and quick cooking.
Sausage is not as cheap, has more spices than a kid's mouth is used to.
Hence, hot dogs took over American summers.
They gave the history of pizza and hot dogs and hamburgers, and it was really fascinating.
(But I don't remember enough of it to know if your theory is correct. :)
Maybe that is why sausages are popular in Britain because we can get quite mild ones almost as mild as frankfurters but IMHO a better taste.