One of the great advantages of overnight travel, whether by rail or coach, is that it affords the ability to save a day's travel. Now, using my home area as ana example (as always!), it's difficulto get anywhere after finishing a day's work. Depending on where you want to go in Europe, you may eb able to find an evening flight that you can ge tto the airport in tiem for, but this will probably mean arriving inw hat may be a strange place at a very late hour indeed.
Alternatively, you can wait until the next day, but catching the early flights from the nearest airport would mean a very early start indeed. In contrast, an overnight train service would allow you to leave in the evening, sleep through the dark hours (hopefully) and arrive with a full day at your destination.
I'm not 100% certain that this proposal would work, and I'd like to see a business plan for it, but it does have a chance if it is aimed at the right market. The fares would have to be competittive, but must also recognise the value that some people place on their time, as well as the fact that it effectively saves the cost of a night's accomoodation.