Bike routing on footways

Issue

Both osm.org and the demo site create a bike route with instructions to cycle on a highway=footway, which is surely incorrect. Bike users should be instructed to use roads or other paths where cycling is allowed or dismount if there is no better/legal alternative.

The issue template mentions profile settings profile settings though I don't know enough about how they work, so I'd be grateful if someone can explain where the issue lies.

Steps to reproduce

https://map.project-osrm.org/?z=18&center=55.960376%2C-3.176760&loc=55.960087%2C-3.176368&loc=55.960510%2C-3.177275&hl=en&alt=0&srv=1

https://www.openstreetmap.org/directions?engine=fossgis_osrm_bike&route=55.96017%2C-3.17596%3B55.96056%2C-3.17699