Drivers already pay for the cost in lost time. It's a 'natural' market.
The main problem with this article is the idea that the goal in traffic policy is to reduce congenstion. No, it should be to maximize utility. Sure, if you reduce roads, add congenstion charges then people will find alternatives to cars. That doesn't imply that utility is increased.
Public transportation is typically worse than using a private car. You can't decide when to leave, you pretty much need to plan your trips around public transportation. They don't take you directly from A to B etc. Public transportation becomes effective only when population density becomes high enough.