This, like many other ideas combining cars and public transport, sounds like something that doesn't scale. The exact numbers vary, but the passenger capacity of a car train is usually something like 1/2 of a normal night train or 1/3 of a normal day train, assuming that the train is fully dedicated to carrying people with cars. You also need special facilities and longer stops, because cars can't just dismount at normal platforms in a couple of minutes. On popular routes, this all means that you take more cars off the road by not carrying cars on the train.
> This implies that rail is running at capacity during the night, which I suspect isn’t true.
cry-laughs in German Oh hell yes we do run at nominal capacity, actually often enough above. The transit routes are fully booked all times of the year, the demand for freight transit is insane, and every bordering country is complaining that we can't get our shit together (to no one's surprise after 30 years of perpetual budget cuts).
The problem is: virtually all trans-European routes run through Germany. You can't avoid running through here.
That's like a lot of half knowledge someone would get by just listening to the media and anecdotal evidence. The net is not at capacity especially not at night. The freight trains that run at night have peak network capacity of only 30% even on high traffic routes like Hamburg - Berlin. There are close to no passenger cars running at night. At least inform yourself before writing a comment in the tonal voice you did.
I do feel like rail in general isn't running anywhere near capacity. If it was optimized better with modern fluid signaling system, "packet based" routing of individual carriages, and way shorter headways, I think 10x the amount of cargo could be squeezed through.
The specialized stops are an issue (and have gotten very rare), but the speed limit from the car train is an issue but especially the highly cyclical nature of the demand for car transport on night trains, much more so than normal sleeper trains. Most of the rolling stock used for transporting cars is very old and not getting replaced (because you can't recoup the cost), while there have been quite a few orders for new sleeper trains.