There's lots of different routing engines built with OSM data. The units they expose are an implementation choice.

The routing engines available on https://www.openstreetmap.org/ (click the bendy arrow next to the search box on the upper left) do return km.

I'm not sure why this stalled out, but it looks like much of the implementation is available:

https://github.com/openstreetmap/openstreetmap-website/pull/...