The idea is interesting but your "minimum speed of 120mph and modern car requirement" is not. Remember, this is rural America we're talking about, that is having trouble keeping hospitals running.
The highways will need to be built on the state/federal level, most transportation is that way.
And did it seem absurd 100 years ago to expect a nation-wide system of 55mph highways?
I'm pretty sure that it did seem absurd, and yet we're all better off for it in the end. Transportation infrastructure has a huge long tail of benefits.