Did the interstate highway system have to buy land rights?

The government used it in Eminent domain power to acquire the land (which if owned was paid for). The interstate system was built by the government, so it’s a totally different situation as the railroads built and maintain the track Amtrack is using.

I guess that then the solution is obvious.

It doesn’t seem like a good use of eminent domain to build a slower and less capable transportation network when airline service is already ubiquitous. “I prefer to spend more for a slower journey because I like trains” is a weak justification for the use of such an invasive power.

I'm not sure what is obvious. The government pays rent on something it didn't build. Cargo is vital to so many sectors of the economy, and passenger trains are not.