Roads are (mostly) not free, and also cost millions of (insert currency unit here) which are covered by taxes. In particular, the asphalted road in a residential street occupied without charge by someone's expensive vehicle is being paid for by, among other people, me -- and as a non-car-owner, I gain essentially no benefit from the provision of this parking space. So clearly, we've opted as a society for subsidizing public services -- but only certain services.
I think the difference is in the perception that roads are static and once built just sort of stay there for everyone, whereas public transit has a lot of running costs. Sure roads have a lot of upkeep cost as well, but it's not as obvious.
Then again, the roads I've seen in the US are so shitty I'm [almost] certain there's no upkeep being done anyway.
The way this works in municipalities or low-population regions of states (which is what most people experience traveling through 95% of the United States' road miles) is that roads are left to deteriorate until such time as they can't avoid fixing, and preferentially might be completely rebuilt which takes a different flavor of money that can be subsidized by the federal govt.
Regions with affluent populations and dense metros essentially have their own road budgets and taxes to keep conditions acceptable.
The other problem in the states is that the weather varies very strongly; this coupled with snowplows and road freight does a number on roads in short order. Some stretches have to be resurfaced yearly. Doing this is expensive and disruptive, so sometimes it is only done in the worst spots if the other parts can wait.
Roads have to be maintained, the cost is non-trivial.
The roads in the US are absolutely a dream compared to say Indonesia, or even China where new roads tend to crumble after a few years of iffy maintenance.
I can think of a few benefits you get from your neighbor's parking space, but the most important is the increased economic output of your neighbor due to their happiness with suburban life.
