The long distance is mostly irrelevant, People use trains daily for short commutes. As for JR, the arguably only reason it was in the position it was in was because the government got in the way. If they'd stayed out of the way the private companies would have built the rest.
Further, JR started private. It was nationalized in 1906. The Tokaido Line and tha Sanyo Line already built by private companies. They forced out 17 other companies and then ran it into the ground.
The only place private "might" not have built is rural and JR built those mostly as "pork-barrel" (favors to politians) when it was run by the government. I also say "might" because it is/was common, not just in Japan, to build housing and trains to that housing. You pick a place like Enoshima, build a few 1000s homes, build a train out there to sell the homes. So "rural" places do get private trains.
Further, JR started private. It was nationalized in 1906. The Tokaido Line and tha Sanyo Line already built by private companies. They forced out 17 other companies and then ran it into the ground.
The only place private "might" not have built is rural and JR built those mostly as "pork-barrel" (favors to politians) when it was run by the government. I also say "might" because it is/was common, not just in Japan, to build housing and trains to that housing. You pick a place like Enoshima, build a few 1000s homes, build a train out there to sell the homes. So "rural" places do get private trains.