I was possible back in the day. My grandfather used to go from 200 inhabitants village in France to Stuttgart in Germany just by walking and taking train. It was possible back then in the 60s, it think it is now.

What they did before cars were ubiquitous was "whistle stops" the train would whistle outside of town to indicate it was coming, and would stop for anybody at the platform otherwise it would continue on without stopping, much like how most buses operate today.

Smaller interurban lines also operated "flag stops" where it would stop when flagged down by a passenger otherwise it would keep going

With EMUs (electric multiple units) and modern signalling service could be brought to small towns fairly cheaply. Most small towns in the US are about 20 miles apart, so hourly service at ~50MPH could easily be provided with a single track mainline and passing sidings only at stations by having one train in each direction every 30 minutes.

The problem is so much money is invested in road infrastructure that investing a similar amount into an equally extensive rail network is simply unfathomable

Switzerland's rural villages are mostly still compact and built around train stations. Just because you're not packed in with a ton of people and stuff doesn't mean that the people and stuff you do have needs to be super far apart.

Granted, stuff is super far apart in the US because that's how we've built it. My point is that we didn't have to do it that way and it isn't impossible to do it better.