Offhand, I can't think of any 'park and ride' style Car <> Transit (train or not) interface in the USA that _does_ charge anything to park there. Finding a spot might be an issue, but there's no cost as that's sort of built into getting someone to take the transit system at all.

As someone else pointed out, any additional friction (multiple transfers, etc) results in a direct all car route.

Most people are somewhat emotionally rational, but the models for calculating the emotional cost (friction) get everything wrong.

Delays past about 5-10 min increase the emotional cost exponentially. Stacking delays (multiple not-user controlled) legs grow even faster. Any uncertainty in the route also massively increases the emotional cost, more so if there's nothing the commuter can do. Contrast Japan's famously well run trains that will even issue an apology the commuter can take to the office of someone else being at fault (I remember this offhand, don't have proof offhand).

Also, the car is more than just getting the person there; it takes their stuff. Abandoning that car leaves behind the potential to move larger items or stacks of things. Plus the car might be critical for visiting friends, stores, etc after work.

All of that factors into the commuter cost.