I did some clicking around in the POS module and found that it is impossible to create payment methods on a POS basis.

I can imagine that there are companies who have multiple stores each on a different location and they have separate accounts for the different payments to get an easy overview how the stores are doing. This basically means that the creation of the payment methods have to be on the POS configuration itself instead of a general one.
If we can agree on this, I will try to make the change.