It's also worth noting that induced demand exists even for public transportation systems. A single rail line can solve the bandwidth problem for a longer time than a new lane on a highway, but if growth continues you'll still end up needing to add new trains and rail lines or add additional modes of mass transportation.

Induced demand is never a reason to leave the problem of bad infrastructure unaddressed, it's just something we have to take into account as we try to improve things.

Adding a passenger rail is in principle not very different from adding a 10-lane corridor. Including the problems of what those people do to enter or leave it, and the fact that it too can become overloaded.

That said, yes, of course the rail is a much better option.