> To me this change to start with the more significant number makes sense. But what led to this change in numbering and when did it take place? Did it follow a longer debate? Was there a transition period?

You could argue we're in a stalled transition period. The teens have not been switched - it "should" be teenthir instead of thirteen etc.

>Could a similar transition happen to other languages like german, where at the moment a "two-and-twenty"-style numbering is in place?

I don't see why not, in principle. Some German books even recommended that in the early days of adoption of the Arabic numerals (which are the reason for the confusion - they go in the opposite direction of original Germanic pronunciation of numbers). Martin Luther wasn't a fan though, and that was probably the deciding factor. It's unlikely anyone will decide to switch it around anytime soon, but not impossible.