It’s not just in train stations—it’s like that in a lot of places.  My guess is that it’s done to reduce swindlery (is that a word?).

Don’s probably right, but I wonder if there is a germ courtesy issue as well?
Money can be filthy (literally and figuratively.)

I was kind of going with the sanitary issue.

In GERMany??(ha ha..) No, it’s just inherent unfriendliness.. Just kidding…

The German habit of shaking hands EVERY SINGLE TIME you meet is hardly sanitary..(I’m an English teacher here.., so I have to shake a lot of students’ hands.. EVERY lesson..) I’m suffering from a terrible cold, that I’m convinced I caught by shaking hands with my girlfriend’s father on X-mas Eve..

With respect to the handing over of money, I much prefer the politeness of Japan, where you hand over a bill with BOTH hands.. And I hate here how they just throw your change on the counter practically without making eye contact..

I suspect the tray thing is because European currency generally has more coins, and it’s just easier to count on a tray than having somebody dump a pile of coins in your cupped hands..

Good comment on Japan.  Toyota is building a new plant in my state and a recent article explained much of the courtesies of dealing with the japanese.  How to take the business card and then look at it carefully and then make a complement about it.
 
I kind of doubt our inbred will take the advice.
 
Rudeness seems to be substituted for strength around here.