You would expect that the surplus of space in many US metropolitan areas would make it considerably easier to install and operate metro transit lines, but this seems not to be the case. I suspect the systemic bias towards road users is much more of a problem than geographical scale.
The point is not lack of space. If the metro station in Europe has 10 times as many people in 1 km radius around it as a metro station in US, you’ll have 10 times as many people riding it. If you have too few people riding it, the capital costs of building the metro (which, by the way, are much higher in the US than in Europe for some inexplicable reason) will be ten times higher per rider. At the same time, low ridership will also result in reducing number of trains per hour to control the costs, further reducing the ridership. The result is that you get a very expensive metro system that nobody is actually using, because most people don’t live close enough to use it, and the train schedules are less convenient than driving.
Interestingly enough there is much more revenue generation for the state in traffic violations. When one is walking or using public transport it’s more difficult for cops to harass them. But people can have a taillight out at any moment that warrants a traffic stop and subsequent fishing expedition. Our urban planning, especially in the West has been heavily biased toward cars.