Actually I think high bathtubs were an American invention when Kohler found that you could put legs on a horse trough and make it into a bath tub. Later in more industrial times America cheapened down to shallow tubs that cost less and only now wealthy Americans are moving towards fancy claw feet tubs. Europe made that move to cheaper tubs much later and that's what most modern bathrooms in European homes have now, just as in America. But older homes may still have the older deep tubs and some hotels do as well. But if you go to, for instance, a newly built Holiday Inn Express in Europe, you won't find expensive deep tubs there.

I'm in a huge suite at a fancy new hotel in France and indeed there is a four legged deep tub in the bathroom. Looks very nice.