Hi RolandP I hear you on all points.
Of all the hotels we booked rooms with, they actually ran our cards fine (meaning we actually were billed, not just reserved). But maybe they’ve got a different system or post-checks of cards or something. Not sure.
My wife tried her Chase card (on sbb.ch, same account as me), and it actually seemed to work once - she got a notice from them, said the charge was valid, and it went through. However, subsequent ones did not. However, we then tried a Citicard, and that seemed to work fine.
Thanks for the pointers!