I'd like when I generate a link, it saved the layer I used.
When I program a routing and want to share with friends, I often use Mapquest layer. I think it is more readable and a better publicity than the default map (OSM must really change this map for public....). And i like my friends see the map as I select it.
This probably won't fix since it cannot be guaranteed that a certain layer will always be available. But we share your concerns about the usability problems of some of the rendering styles.