Yes, the main benefit of trains and proper buses is that you wont get stuck in traffic. So in the worst case scenario you'll see troughput increases as a function of ridership (more occupancy, more trains) while trying to battle overcrowding. By adding more trains and buses. Trains have another benefit to the population that they can travel at higher speed, so the induced demand with trains can get even higher because of the large distance you can travel if you travel at 200+ kmph.

Induced demand isn't actually a bad thing unless your transportation gets less efficient the more people use them. Which is definitely the case with cars. Just look at the amount of parking spaces needed to cope with peak hours. This can all be avoided if trains and buses are a viable and comfortable option for people.

Just think about the average car ridership only having 1.2 passengers. While a bus that takes up three parking spaces can have 50-100 people. Or a train that could hold up to 1500 passengers.

Exactly. That's why tram+bike combo in Netherlands is so effective. People travel big distance by train and small distance to work, home and shops. Since trams are very efficient at moving a lot of people car congestion will be reduced. If number of people using trams increases more than their capacity, surprise, you can add another section without hiring one more driver. So big capacity transport that can be adapted to demand and that has priority on the road(it's own lane) and is frequent enough basically can satisfy most of the traffic human needs

This could be, but usually public transport is more effective. Eg. A Bus can transport 4-8 more people, than a car for the same space used on the streets. This rate is even more increased with trains or trams. Therefore people need to demand 4-8 times more public transport than with cars to equalize the effects.

This holds true as long as the population is constant, becaus a single human can not spend an indefintly amount of time in public transport.

If the population can increase eg. Housing Markets in cities, this wont work. If you could double or quadruple the amount of available houses instantly the demand would also go up after some time…

The scaling curve of a tram or bus is very different than for cars. A bus takes up about as much room as 3 cars and holds up to 200 passengers. The typical car at rush hour has 1 passenger.

You can pack a lot of buses onto a bus lane. Trains and trams scale even better because you can expand the same vehicle by adding more sections.