The US is special because its cities were either built to be pedestrian-hostile, or were made so during the Depression years when the transport companies went bust.
Now, in addition to the mindset shift, I think you'd need to rebuild entire cities/metroplexes to make the public transport work.
Case in point: the South Bay Area, where I live now. Sure, you can add trains (at a huge cost). But once you get off the train station, where do you go? The sidewalks are those narrow strips separating the roadway from the parking lots adjacent to stores, they are no joy to walk on, and it will take you forever.
Where in Europe you have:
[store][sidewalk][roadway, 2 lanes][sidewalk][store]
Here, you have:
[business][parking lot][impenetrable hedge][sidewalk][roadway, 3 lanes][uncrossable median][roadway, 3 lanes][sidewalk][impenetrable hedge][parking lot][business]
Then, due to the zoning regulations you don't have stores and cafes right next to place where people live - you have huge blocks with nothing in them but houses, houses, houses.
Ditto for business districts.
It's not enough to have public transport, one needs to rethink entire cities from ground up to make them walkable, bikeable - and accessible by public transport - even if it exists.
Another case in point: Seattle. Lacking a good train system, they made the buses work with dedicated bus lanes, which make the buses fast - faster than traffic.
This works because the city has not been developed in the sad way I described above.
As for the suburban wasteland, which makes up huge chunks of the US population-wise, you can throw all your trains and buses at it, and it will be but a drop in the bucket.
Disclaimer: lived half my life in the US, half my life in urban Ukraine. Big fan of public transport, but drive most of the time - and when I don't, I bike, outrunning public transportation in most cases on distances up to 6 miles or so.
EDIT: see the urban sprawl point below:
> The US is special because its cities were either built to be pedestrian-hostile, or were made so during the Depression years when the transport companies went bust.
The original argument is based on "nature", things outside of human control. Your argument is 100% under human control, a self-made problem. What perplexes me is that the "nature" (inevitability) argument always comes first, but when prodded (like I did here) there is the attempt to shift it it elsewhere. I don't like that style, as I said, this seems to be mostly emotions-driven and I don't quite get why there is this attempt at any cost to paint the US situation as "special". Everyone and everything is "special" if you dig deep enough. The point is, are the difficulties any worse than elsewhere in magnitude and complexity? I don't think so. You only argued about the US, but the point of "being special" here has the meaning of "it's more difficult", and I don't think that is justified at all.
As for your question:
>are the difficulties any worse than elsewhere in magnitude and complexity?
I firmly think that this is the case - a century of bad urban planning is hard to undo. You don't have that in Europe (cities are old, the layout makes public transport viable and necessary), you don't have in 2nd world countries (a lot of growth happened under central planning that bet big on public transport because it couldn't provide enough cars for its citizens).
Huge cities in the US are different from cities in Europe. Even when a European city has suburbs, taking a train to the city center makes sense because you can get around the city center without a car. That is not the case in Houston or Dallas, for example. You wouldn't want to walk there.
Yes, these problems are man-made - but they are entrenched and systemic to a scale that I'm unaware of.
I guess what I am saying here: we need to understand the scope of the problem. It's not that it's more difficult to make trains running in Dallas than it is in Paris.
It's that we need to rebuild Dallas from ground up for that train to make sense there due to the way it grew in the past 70 years.
TL;DR: screw-ups are hard to undo.