Thank for all the input so far!
So the EuroNight train to Prague travels northeast all the way to Berlin from Cologne before turning south towards Dresden and Prague? Seems like a very circuitous route.
I recall a night train operating between Amsterdam and Prague via Leipzig (thus, avoiding Berlin). However, that train was cancelled in the early 2000s. Dutch Railways closed down its sleeper train business then.
Since, then Deutsche Bahn was in charge. For many years, there was no Amsterdam/Cologne-Prague night train at all. In the late 2000s Deutsche Bahn decided to extend its Cologne sleeper service from Dresden to Prague. Since that train called in Berlin, the extended train would call in Berlin, as well.
It is not possible to (officially) book a ticket in the through cars Cologne-Warsaw from or to Berlin. Hence, no passengers get off or join the train here.
What's the rationale for this? If they're going to stop in Berlin HBF anyways, why not make it an official stop?
the official explanation: Berlin pax should not disturb the through pax (Cologne-Warsaw).
However, the truth is somehow different. Both Deutsche Bahn and PKP Intercity worked very hard in tandem to make the EuroNight Jan Kiepura as unattractive as possible. Hence, giving them the excuse in the end to cancel the service.
In 2007 you could easily book (and print) an e-ticket for the Amsterdam/Cologne-Warsaw train in both directions. In 2016 -> that was not possible. It was done by design. You need a paper ticket. You may order it online, but you need to wait a couple of days for it to be delivered by post (which you need to pay, as well).
This is 2016 -> you can book an air or bus ticket within minutes online - not so for the railways.