The problem is that you don't pay for the slowdown you cause to everyone else. You're offloading that cost, so you keep choosing to use the road well beyond the point where traffic should be increasing.
To make up for that, we can charge people at the entrance point. But charging people time is basically impossible, so money is used instead.
Therefore more roads => more cars => same trip times. I could see that people would make decisions to take jobs where they travel by car, or choose to live further away etc. with more tunnels. That could be a good thing or bad, but yes the demand will increase, because people will find new reasons to get about if there is more road to do it on. Let alone business use of roads.
If you had to pay for road access, you could easily set the price to where demand meets supply, and all roads would have well flowing traffic 24/7.
But of course "induced demand" happens when the price is $0. The same would occur for bread, phones or pianos at that price point.