> However, OpenStreetMap’s own servers are run entirely on donated resources. They have strictly limited capacity. Heavy use of OSM tiles adversely affects people’s ability to edit the map, and is an abuse of the individual donations and sponsorship which provide hardware and bandwidth. As a result, we require that users of the tiles abide by this tile usage policy.
The default OSM tile server is not here to serve your startup.
As I've said, the solutions are there, and there is an actual demand for cheap vector tile hosting without all of the other cruft that is bundled in the commercial solutions but isn't actually needed.
Fortunately there’s a large selection of background layers for leaflet: http://leaflet-extras.github.io/leaflet-providers/preview/ I quite like CartoDB Positron for as a muted background.