Look at it another way:
We assume the unit cost of laying tracks is the same, and that some track can be shared for country B. We also assume GDP is the same for both countries so the important statistic is length of track only
Square country A has two major cities, each of population P, which are located at the opposite corners of the square. The area is X^2. The distance between the cities is sqrt(2)X.
Square country B has four major cities, each of population P, which are located at each corner of the square. The area is X^2/2. The minimum required line to connect is about 2sqrt(2)X/sqrt(2), that is 2X
Granted, it's a simplistic analysis for illustrative purposes but shows that the balance of costs isn't necessarily the way you are assuming - that is it's actually probably more expensive for Europe. In this example, the larger and more sparsely populated country has to spend 1.4 times as much. This ignores revenue from ticket sales, of course, So let's assume that it's twice with twice the population, now the larger country spends 1.4 times as much per ticket sale. But that's not 2.5:1 as you are suggesting as the important ratio. Given that USA:EU GDP is 3:2, the 1.5/1.4 is 1 - i.e. in proportion to GDP it would be a wash. Obviously, the exact details are different but given that the cost of land is a large part of the cost of building rail links and land is cheaper in the USA, then it's not obvious that it should be hard for the USA to build high-speed rail if it wants to.