The alternate route after Leon through Villa de Mazarife is nice. We really enjoyed that route. Some of it is road walking, but they are quiet roads. Most of the time you are on paths that cut across the countryside though.
Regarding road walking in general - it seems that most of the time, if it was a busy road, there was a gravel path next to the road for walking. If you were walking on the road itself, the roads were not heavily traveled. And there are some places where you can take alternate routes away from the road. We had Bierley's guide and they were usually shown. One that I am thinking about is the walk from Fromista to Carrion de los Condes, which is mostly along a straight gravel path next to a road. But, you can take an alternate route that follows a small river. The route is pretty much parallel to the road and sometimes you can still see the road, but you are a couple hundred meters away, with trees and nice paths. It adds a couple km, but the walk is very pretty.
Another section with a lot of road walking was just after Villafranca al Bierzo, heading up to O'Cebreiro - the main route is road, except the last 1/3 or so - but it isn't so busy since another highway was built to take the traffic. I think this section used to be sketchy, but now it is ok. And although it is road walking, you go up through a nice river valley, which is quite scenic and nice. But there is another route you can take out of Villafranca that kind of parallels the main route on paths and quieter roads - it climbs up out of the river valley, so you have more elevation gain, but it is an option to avoid the road if you want to.