OSM suffers because everyone creates his own (closed source) layer service and his own (closed source) routing service.
Instead the community should be on the OSM site and contribute to open layers hosted on the official page and open routing code so that the OSM map data can be tuned for it. But apparently it goes in the opposite direction :(
What you see on cycle.travel _is_ an open source router. They run https://github.com/Project-OSRM/osrm-backend
Actually, I don't really see where you get that impression from. Very few commercial providers use their own routing stack. It is almost always OSRM or pgRouting if you want something that scales for world-wide routing.
Instead the community should be on the OSM site and contribute to open layers hosted on the official page and open routing code so that the OSM map data can be tuned for it. But apparently it goes in the opposite direction :(