No, it's because no one wants to live "in" the city. Too crowded and expensive. So they move a little bit outside the city and commute. But then they want their stores and restaurants closer to them, so stuff springs up around the suburb. Then that gets to be too crowded, so they move a bit further out of the suburbs,
ad nauseum.
It's why Wake County, NC has a population of over 1 million without having a residential building more than 14 stories tall (and very few of over 4-5 stories).
Only in a few places like New York or Chicago do you find cities that build up rather than out. When new cities were being settled, land was cheap and plentiful, so cities grew out rather than up. In Europe, most major cities have been inhabited for 1000+ years, and their footprint was often constrained by things like old city walls and fortifications. Sure, there's additional sprawl beyond them now, but you don't see suburbs dotting the countryside in many parts of Europe.
Compact city footprint = better viability of mass transit. Consider this:
Raleigh, NC -- population 416,468. City area is 370 km
2. It's about 20 miles across from east to west.
Population-wise, it's about the same size as Bristol and Brno, but about 50% larger in area than Brno, and over three times the size of Bristol.
In terms of area, it's on par with Leeds/Bradford, Glasgow and Dublin, but with less than 1/3 of the population of Leeds or Glasgow and about 40% of the population of Dublin.
Raleigh's a pretty average American city in terms of its "sprawliness". I live near the edge of the city and work just a couple of miles from downtown. My morning commute is 10 miles. Hell, my second girlfriend works in Raleigh and lives
in another county. Her commute is 35 miles each way. My first girlfriend is considering taking a new job that would pay significantly more but mean an hour commute of about 44 miles, if traffic isn't bad. That's nearly 90 miles a day just getting to work. That's a little extreme, but you see what I'm saying. We drive a hell of a lot in the US because we kinda have to.
Just extrapolating from these examples, cities in the UK are basically three times denser than American cities (obviously, not taking into account outliers like London and Smithwyck-on-Farthing-Tweed, or New York City and Lizard Lick...yes, that is a
real place.)