Such trains have existed for decades already in at least Finland and they certainly haven't killed airlines. Even though there are many advantages: You can put all your stuff in the car when leaving home and at your destination you get to use your own, familiar car instead of a rental car that would also cost more.
Here's a link. Also, pictures of car and truck carriers being switched at the station, waiting to be coupled onto a night train.
You can see three types of vehicle carriers; the blue and white double decker with an open upper deck, the red and white fully enclosed double decker, and the flatcar truck carrier, which is also used to haul charter buses. All of these are loaded and unloaded with an end ramp, and can be driven through. They are set out for unloading, and loaded ones are picked up, i.e. the loading has to be complete about an hour before the train arrives. The vehicles are held in place with their own parking brakes plus wheel chocks.
...and no, they haven't killed airlines, but they certaily are booked to capacity. However, there have been talks about closing down some provincial airports because of insufficient customer base (a few thousand passengers per year). It seems that fast rail connections have made the airlines somewhat redundant, and one airline's messing about (charging for flights and then not flying) has not done much to help, either.