OpenStreetMap folks just care about the data, I doubt anyone would begrudge someone making a proprietary service using open data - it's the data that's important, after all. The OSM Project is not looking to replace Google My Maps, or to have such a service on the main osm.org website.

Now, what you are looking for is probably something along the lines of uMap http://wiki.openstreetmap.org/wiki/UMap which has something like a WTFPL license https://github.com/umap-project/umap/ and which is something I point people to. It's lacking the design flair of this product but it's probably a bit more feature rich.