Before I get into this, a bit about induced demand:So let's take an extreme example then. Iet's say the 401 was left as a 4 lane highway like when it was first built. Would it still be able to carry the volume it does now? No. That traffic would have to go somewhere- it doesn't magically disappear. Yes some could be taken away by better transit but you'd run into severe congestion on the highway possibly stretching hundreds of KM. All the other roads in and outside Greater Toronto would also become clogged and the economy would grind to a halt, especially any kind of industry that relies on trucking.
Ideally, road and transit projects need to keep pace with growth. Induced demand is a thing so yes lesson learned when they jumped the 401 from 4 to 12 lanes. If you build it, they will come. It could have been expanded more slowly to keep up with demand but that may have been more costly in the long run. At least highways weren't built everywhere like in many US cities.
There are only two (major) things that will discourage someone from using a road: traffic and tolls. I will ignore tolls, since the 407 and 412 are the only toll roads in Ontario. If there happens to be no traffic on a non-tolled highway, people will move further away from their work, make more trips, etc. because there is now nothing to discourage them from using the highway. Developers will take advantage and build more subdivisions near the highway. As a result, the highway becomes congested because of its own existence. The highway will always be congested, as long as this highway is located in a successful major city. If the highway is widened and traffic reduced, the same thing I was talking about earlier happens again, and the highway becomes congested again. In a successful major city, demand for mobility is almost always much, much higher than supply. There is an enormous amount of latent demand. Thus, as soon as supply increases, the latent demand quickly comes to fill that newly created supply.
Now back to the 401 example:
If the 401 was never expanded past 4 lanes, yes there would be traffic. Yes, a 4 lane highway carries less cars than a 12 lane highway. But, if the highway was never expanded, the traffic would disappear (not magically). In fact, it would never exist in the first place. Just as induced demand is true (if you build it they will come), the inverse is equally true (if you don't build it, they won't come).
Think about why the 401, even though it is an enormous 12 lanes wide, is so full of traffic. Why are there so many cars?
The reason all 12 lanes are full of traffic today is because there are 12 lanes. If the 401 (and for that matter, any of the other highways in the GTA) was never expanded or built, we would never see the vast expanses of car-centric suburbia funnelling traffic onto our roads. We would not see people living 30+ km from work and thus having to drive that far. The entire built form of the GTA would be different to reflect the fact that there is less highway capacity
Road projects can (almost) never keep up with growth in a successful large city. Growth (in traffic) increases because of road projects. Roads can't be expanded indefinitely due to space and money constraints.
Now, what about transit?
Transit projects face induced demand too. Part of the reason the Yonge line is overcrowded is also due to its own existence - for example, all of the development along the Yonge corridor and the people that make travelling decisions due to the existence of the Yonge line. In big transit-centric cities like Tokyo or London or Paris, the system is always overcrowded, even after huge expansions.
However, there is a very important difference between transit and roads: transit is much more efficient. I mentioned earlier that the constraints on road-building are space and money. Transit building faces the same constraints. However, assuming both the roads and transit are equally intelligently planned, roads require far more money and far more space than transit to carry the same number of people. A transit vehicle simply moves more people in a smaller space. Transit can be built in far more different corridors than roads because it is much cheaper and easier to build underground or elevated transit when compared to underground or elevated roads, so far more transit lines are built. For example, the Bloor-Danforth line takes up much less ROW and carries something like 4-5x more riders than the DVP despite only being about 2x longer. As another example, a mid-sized car-centric city like Indianapolis has traffic issues (looking up "Indianapolis traffic congestion" yields many results), but similarly sized transit-oriented cities like Marseille do not have similarly bad transit overcrowding issues (looking up "Marseille metro overcrowding" doesn't yield anything relevant). Although not a perfect comparison, this shows that with similar resources and population, transit investment goes further in moving people.
I didn't really know where to add this so this will be at the end, but transit also has another huge advantage - when road users increase, very quickly everyone's journeys get much slower due to traffic. But, with transit, as ridership increases, riders may be less comfortable, but speed does not decrease nearly as much.
Note: Self driving cars and increasing road efficiency
Self-driving car stuff seems to be popping up on other threads here. It is true that the widespread adoption of self-driving cars will dramatically increase road capacity by increasing efficiency. However, this increase in capacity is not fundamentally different from the increase in capacity from widening roads. Induced demand does not change. And, the core problem of cars taking up more space than transit and thus costing more remains the same - transit infrastructure will still be more efficient than roads for self driving cars.
Apologies for the long post!