Let's see. Cologne to Berlin takes ~4:40 hours by train. Flixbus takes 9-10 hours, not counting the time it takes to get to their departure station which would involve a train journey as it's not actually in the city centre.

Flixbus is 50€ cheaper when traveling that route tomorrow but that's about all it has going for it.

1 hour by plane (+ time hanging around the airport, but train/bus has the same issue there)

Train and bus normally have that “10-20 minutes ahead” planning to be at the station.

Planes? At least an hour, and if you cut into that, and the queues or security theatre more mind boggling than normal, you’ve missed your flights.

Eurostar is similar to airports, so I’m glowering at them too!

Even if you aren't at the airport that early, it still takes you an hour to get from the airport to the city centre in Berlin, and about half an hour to get to the airport from Cologne's city centre. That's by train, by car it takes even longer.

It depends if you're going from "centre to centre" or "somewhere near Cologne to somewhere near Berlin".

Sure but assuming you're traveling from centre to centre, which is where population densities are highest, is a sound assumption. Otherwise you can always find spots where getting to the airport, train station, flixbus stop or whatever takes extremely long with one mode of transport over the other.

Doesn't distract from the point that long distances busses are very much not an alternative to rail (or planes for that matter) unless price is the deciding factor. And even the latter is questionable in many cases thanks to the 49€ ticket.

Also no time at all when arriving. Getting out of a train and the station rarely takes more than five minutes; usually less.

The 50eur pass doesn't include the trains you'd use for the trips you'd use Flixbus for.