Ben T's GPX Editor (which uses Google routing) doesn't stray off-road if you set it in car mode (or at least I've not found it to do so).
it hasn't got user editable routing though
yet
Hey, you've given us a choice of four modes, quite enough for most folks.
Somewhat drifting OT, but whilst we are comparing routing.....
On one of my local quick routes out from suburbia into the countryside, there is a corner that can be cut in a variety of ways, or could be if not for some No Cycling signs (and some awkward chicane barriers).
Taking the road as "nominal" both cycle.travel and the bike option on GPX Editor take a path that cuts off about 150 mtrs.
The walking option on GPX Editor takes an addtional section of path that cuts off a further 100 mtrs.
Surprisingly (in view of what Bianchi Boy says) Velomap takes the road..... which, because of the barriers, is actually the most practical option.
The other thing I found a little odd is that the two sections of path appear to be same category in Google, and have the same tags in OSM (Gr 2 path) so I'm puzzled why one should be selected in "cycling mode" and not t'other.
(Route from N 50 59.825 W 1 23.487 to N51 00.203 W 1 24.289 if anyone is interested in looking into the nuts & bolts of it)