This better than every wealthy person owning an RV. Though there is still the last mile problem. Does my personal train car have a vehicle on board (probably I’m rich in this scenario)?
Groups of wealthy people could split a train car. Private Train-car time shares?
I was thinking you could just park one of those small 'air taxis' to the top of the train car (allowing clearance for tunnels and bridges).
Unless you’re transporting something like the president‘s personal limo, the beast you just rent what you need at your destination.
When you get to the “pay someone to drive the car to where you need to be so that you can use it” amounts of money things become much easier.
If you're actually wealthy, you don't have to split a train car.
Last mile problem? Have your personal assistant drive whatever vehicle you want and have it waiting when the train arrives. They can take an Uber back to wherever they need to be next.