We do actually. The German Girocards were, until Maestro ceased to exist, often co-issued as Maestro + Girocard, and global acceptance was pretty good under the Mastercard network.

There are examples of other co-branded national payment systems out there (troy + Discover comes to mind).

If a European payment system (with cards, at a store) is to exist, then visa/mc will still want a piece of the pie by at least playing along to remain as a co-brand and taking their cuts from international payments.