Thanks a lot !

Yes, the routing provider is completely independent of the currently used map layer.

I think I might get what you mean - that with Google, the routes should conform to the tiles, but when using non-Google map layers (such as Mapnik), it might suggest a route that is not visible on the map. IMHO, seems to be not that much of an issue as at least with Turn-by-turn navigation, correct directions are much more important that a little inconsistent map layer.

When more online routing providers are supported, automatically using a provider corresponding to the given layer (Google for Google layers; OSRM & company for OpenStreetMap layers) might be a good optional feature.