Am German, can confirm. Parking garages do indeed exist here. Germany is very car centric, but fortunately not as bad as the US. Our cities do also have mostly working public infrastructure that makes it possible for lots of people to get to the Christmas market and drink several mugs of mulled wine without the need for overly huge parking garages.
I agree, there’s definitely room for improvement.
It seems rare, that the whole train station was closed (probably not one of the bigger cities) and you must have stayed rather late, while christmas markets usually already open in the afternoon (or even earlier) and the sun sets early in their season, so there’s plenty of time to enjoy them while they are most beautiful (at night) and still make it home by train in a lot of places.
That being said, in more places than you’d expect, you won’t find convenient train connections after midnight, if at all. That makes using public transit almost useless for partying. I remember living in a somewhat rural area as a young partygoer and if I wanted to go to the city for partying, the choice was to either go home before the city folk even really started going, or keep partying until the clubs closed and then hang around with the punks at the railroad station to wait for the first train in the morning. Having a designated driver and going by car was the usual option.