I have visited every country in the EU, a lot of which by train, it has been a thing my friends and I have done over the last 10 years, going to a few countries each year, trying to use public transport where it is reasonable. Along the way, I have been on a number of overnight trains and a number of overnight ferries and I personally highly rate the experience. There is something almost romantic about falling asleep one place and waking up somewhere else. But also the social aspect, head down to the bar cart on the train, have a beer, chat to other people, most people are a lot more open to chating than normal and you find out about their life, their reason for travel and sometimes even end up seeing them once you arrive at your destination. On top of that, planes are typically really noisy (from the engine), cramped, and just difficult (okay, business class is a fair bit better and I can only assume 1st class even more so) where as the train is quiet and just a nice way to relax either on the way back from somewhere on to build the excitement when heading somewhere!
Then again, I have also travelled the length of the Trans-Mongolian railway (St Petersburg to Beijing) and across the States (California to New York) by sleeper train!
I did it about 10 years ago when I was a student, I left the day before, with a backpack, a rough idea of the itinerary and a few tourist guide books, and visited in the course of 3 weeks Bruxelles, Bruges, Amsterdam, Lubeck, Copenhagen and Berlin (and a small stop in Cologne).
Definitely something I would recommend to any student in Europe.
Then again, I have also travelled the length of the Trans-Mongolian railway (St Petersburg to Beijing) and across the States (California to New York) by sleeper train!