I have yet to find an Online Cycle routefinder that takes cyclepaths to detour busy roads and junctions.
Personally, busy roads don't bother me, but they do bother some cyclists.
The problem with Online routefinders is they use mapping and software that was constructed for the Motorcar community. Some have 'avoid motorways' for learners and scaredy cats.
I use mapsource Topo GB.
It shows contours, so when I see the route is up some densely packed lines, I check other routes by putting in a viapoint along another road.
I have found from experience the shortest route turns out to be the best, however steep it gets. Going round may eventually be longer in time as well as distance.
For instance, the first section of Beacon RRC Audax from Wythall to Broadway Tower. The recommended route goes round and climbs a 10%.
The direct route is 3 km shorter but has a 14% for 200 m.
Going up the 14% ( walking ), I got to the control minutes before the group.
To these ends, I plan a route on Metroguide and check the hills on Topo GB. Then I know when to swig and nosh.
BTW, Bikehike doesn't know there is a cyclepath across the Severn Bridge. Its a bloody long way round from Bristol to Chepstow if you don't do some extra research and rely solely on an internet routefinding website.