Let's say Western Europe = Germany, Austria, Italy, and everything west of them, i. e. Benelux, France, Switzerland, Spain, Portugal, Great Britain (= UK - Northern Ireland). (I'm including the UK and excluding Ireland because there are rail connecctions from Britain to the mainland but not from Ireland to Britain. I'm excluding Denmark because isn't that really Scandinavia?)
Total population: Germany = 84m, France = 68m, Britain = 66m, Italy = 59m, Spain = 47m, Netherlands = 18m, Belgium = 12m, Portugal = 10m, Austria = 9m, Switzerland = 9m, Luxembourg = 1m. Total is 383m.
Total area, in km^2: Germany = 358k, France = 551k, Britain = 228k, Italy = 301k, Spain = 499k, Netherlands = 41k, Belgium = 31k, Portugal = 88k, Austria = 84k, Switzerland = 41k, Luxembourg = 3k. Total is 2225k.
So the population density of western Europe is about 172/km^2 or 445/mi^2.
The only states this dense are DC, New Jersey, Rhode Island, Connecticut, Maryland, Delaware; New York and Florida are just under the cutoff.
If I've done the math right, DC + NJ + RI + MA + CT + MD + DE + NY + PA + OH (74m people/429k km^2) is the largest contiguous bunch of states which is over 172 people/km^2.
If we take the east to be everything east of the Mississippi, I get 190m people in 2.301m km^2, or 82 people/km^2. If we add in CA + OR + WA that actually drags down the density a bit.
So the densely populated bits of the Northeast/mid-Atlantic are as densely populated as Western Europe. But the eastern US as a whole isn't.
I agree that those pairs of cities you mentioned should have better connections between them though.
Does regular bus service not count? Sure they're not publicly owned but does that result in any meaningful differences to the users?
Western Europe's population density gradient is much sharper than most of the US. Only the coastal corridor of the Northeast US really comes close. The gradient of the populations is important because it tells you how many people are within a usable range of the train stations.
Even if you've got a high speed line between Madison and Milwaukee what in the hell are you going to do once you step off the train? Neither city has impressive public transit and both are very spread out. A high speed link might save a boring drive between those cities but that savings would get eaten up by the intra-city travel.
I just spent 7 weeks traveling around Europe by train. I would not have considered that approach without the extensive local public transportation systems. Atlanta is not remotely in the same league as Berlin in terms of public transit.
There's no good reason for us to have zero public transit options between Atlanta and Savannah, Madison and Milwaukee, Columbus and Cincinatti, Denver and Colorado Springs, or Mobile and New Orleans.