I wouldn't want to talk you out of going a city you'd probably enjoy. It is a great city and worth seeing, it just doesn't seem to fit into your itinerary very well. Also taking the right route through Austria and Bavaria can be the textbook definition of "picturesque"
On my last 4 trips I spent maybe 1-4 days in each city and that seemed to work well. A grand tour like I'm proposing of the main western European capitals seems like it should warrant a bit more time per city than that.
And I know that if I go to Paris, I'll just want to see the main sights and move on, so that would require maybe 2-3 days of time.. London? I just really want to go to a Chelsea game, see big ben, buckingham palace, and that's really it. I mean, I haven't done my research, but.. I will really probably want more time to explore cities like Berlin, Prague, and Amsterdam.
It really seems like some cities I am going to fall in love with and want to spend more than 2-3 days in, and some I will want to just move on from.. So maybe a trip like this can't really be planned planned - aside from a very rough guide, an arrival date, and a departure date.
I also wonder if I could guy some sort of a month-long rail multipass that would allow me to jump from train to train after having paid just 1 fee for the whole trip.
There's nothing wrong, too, with doing a "grand European tour" kind of thing- I did something similar, about 2/3 the length and more Central European, a couple of years ago- as long as you don't turn around afterwards and consider Europe "done"
Oh, of course not. I have plans to at some point do a tour of Scandinavia, as well as a separate visit to Croatia, Hungary, Austria, etc. The only places I've seen so far are pretty much most of the main sights in Poland, and tiny bits of Germany.