It might work, but not in the US.
I think that such a system would work OK for societies where the majority of
people do not have individual transportation so that the volume might make it
economical.
The problem with mass transport is that it rarely goes to where you want it to
go at the time you want to go. Trains are fantastically efficient for cargo, but
the costs to an individual usually make planes a more sensible option for long
distance, and buses for shorter trips.
Likely you could solve more of the problems related to the trains by simply having smaller trains using smaller, more cost effective engines and having them run more frequently. Some trains would get overloaded, but if you have a good ticketing system the additional 15 minutes would be a price many would be willing to pay for lowered costs. Also, if you have trains that did not need to make as many stops, that would
likely help.