We have worked fairly extensively on automated routing software and solutions for delivery routing in Ireland. This includes the Google Maps and Routing APIs, Leaflet, Mapbox, Openstreetmap and OSRM.
Unusually, we have our own routing servers, able to provide automated routing for over 100 waypoints and stop overs. This gets past the 'Google' limit of 23 waypoints.
Integration of the routing / trip /directions service into other applications we develop is trivial. Typically, we would still use the Google Maps API as a front end, simply for familiarity and because it has excellent traffic management.