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.
1. the observation that, AFAIK, there are no instances anywhere in the world where adding roads or lanes to roads resulted in over-capacity for the roads
2. your claim that this is because of existing demand that was not previously being met
This would appear to imply that the existing demand - which I'd like to call "implicit demand", because it was not visible via behavior until the roads were expanded - is in fact so large that to meet it would require building a road system of so vast a scope that we clearly would not want it.
Put differently, if building roads merely exposes existing demands, and the 10-100x fold increase in roads over the last, say, century, has not yet met those demands, then we should conclude that it is either impossible to meet those existing demands or will require basically the total destruction of so much land that it will be untenable.
Allowing outdated and inadequate infrastructure to make people miserable and hinder a thriving local economy is a terrible idea. Improving and adapting our roadways to meet the needs of a growing community is exactly what we want cities to do. We shouldn't use induced demand as an excuse to neglect that responsibility, we just have to understand the effect so that we can plan for it.