Ironically it’s other way around. The reason why flights are so cheap is because they are privatized and there is heavy competition. US used to have heavily-regulated air travel. Once it was de-regulated prices went down.
Since railroads require very expansive infrastructure, have natural competition limitations (two companies can’t send two trains on the same path at the same time), they are heavily regulated, and as such there is less competition, and thus no invisible hand of the market helping to lower the prices.
Since railroads require very expansive infrastructure, have natural competition limitations (two companies can’t send two trains on the same path at the same time), they are heavily regulated, and as such there is less competition, and thus no invisible hand of the market helping to lower the prices.