> I think the use case of this kind of train is more similar to a flight with one or more nights at destination, so that the specific arrival time is not that important.
OP was explicitly comparing car and trains, not flight and trains.
If that's the case, then we are more in the context of a "city trip", and Hamburg -> Berlin might not be the most representative case. Something along the line of Hamburg -> Rome is more accurate as people usually like more change of scenery. Flight from Hamburg to Rome is 2:20 and train is 19 hours. Even accounting for airport wait time, the difference is ridiculous.
The issue for passenger transport with rails is that it's not good for small distances as cars have the advantage because of the added convince/flexibility, and for long distances, flight is better due to speed.
For freight, however, train is amazing as these extra hours don't matter too much and the reduction in emissions is massive. The issue is that there aren't that many dedicated cargo flights. Most cargo revenue come from transporting freight in the holds of passenger jets. So moving cargo from flights to trains does not lead to a direct reduction in CO2 emission since those planes are going to fly anyway.