Population density is critical for the economic viability of passenger rail. The track costs the same whether there's one train a day or 200 trains a day, and a full train only costs slightly more to run than a nearly empty train. Share out the fixed costs across more passengers, and the rail system can turn a profit at a much lower fare. It's also just plain more useful to any given prospective passenger if there's a denser network of tracks (more likely there's a train that goes from somewhere close to where you are to somewhere close to where you want to be) and more frequent trains on each track (it cramps your schedule less when there's a train every 10 minutes than when there's a train every 2 hours). All of this is much easier in a dense urban area (for commuter rail) or running between urban centers (for long-distance passenger rail). This is a big part of why the NYC subway system is much more successful than, say, CalTrain.
If post-war America had invested heavily in rail in the 40s and 50s rather than in roads, it's likely cities would have stayed dense. Expanding a rail system to support wide-flung suburbs is much harder to do well than building roads, and the marginal benefit of attempting to do so is probably significantly less than improving service and capacity within the existing urban area (which generally isn't practical for roads, since roads are much less land-efficient than train tracks if each is operating near capacity).
An interesting side effect would be that there would have had to have been a different solution for the post-war housing shortage. OTL, suburbs sprung up, with detached single-family houses being mass-produced on cheap farmland which had just become (thanks to the newly expanded and improved highway system) a short drive away from the nearest city. Without the highways, Levittown and the like don't really make sense to build. Instead, there's be some combination of more and earlier high-rise construction in major cities, and cultural shifts towards increased adoptions of living patterns that make more efficient use of scarce living space (multigenerational households, roommates and boarders, or even dorm- or barracks-style housing for young adults living away from their families).
I'd be interested to see what happens to rent control in such an environment. On one hand, price fixing causes artificial shortages, and abolishing rent control would be the most economically effective way of getting developers to start building up the cities to accommodate demand for housing. On the other hand, the inherent expense of urban land and the cost of high-rise construction (combined with pent-up demand while waiting for construction to catch up) would likely cause severe sticker shock among renters, potentially expanding the political constituency in favor of preserving and expanding rent control.