The fastest 'high-speed rail would, in fact, need to be between sizeable cities only.
But, there could possibly also be trains running on the same lines that travel at similar speeds but make more stops, thus taking longer.
As an example,
I frequently use the Shinkansen when I am in Japan.
When traveling from Kyoto to Tokyo..
The distance is about 275 miles.
There are three speeds of trains on this line-- the Tokaido Line.
The fastest is the Kodama, which makes just 4 stops- Nagoya, Yokohama, Shinagawa and Tokyo Station. --- Secret-- unless you REALLY need to go to Tokyo Station for a transfer or some other reason, get off at Shinagawa. :>
)) ---
It takes about 2:15 to Shinagawa. and for a reserved seat costs about $120 one way..
The slower trains are cheaper. The slowest train makes about 15 stops and takes some 4 hours. (Driving takes about 6 hours and cost much more due to tolls and petrol.)
PLUS-- you don't have to worry about getting to an airport 2 hours early, standing in lines, security, cramped seats, bad weather, 'equipment' problems ( very, very rarely in Japan, anyway). Getting from the airport to the city... Plus the seats on extremely comfortable...
So, this might be one option to consider... trains with more or less stops.. (BTW, stops on the Shinkansen are FAST... 2-3 minutes. Do not linger.)
So 'high-speed' rail will not 'solve' whatever the problem is in the rural areas of the country, but it certainly would be a boon to a large percentage of the population where it is feasible, which could include smaller urban areas in otherwise 'rural America..