A case can be made for off carriageway cycle paths on new NSL dual carriageway trunk roads I think, particularly at junctions with slip roads. I'd support that case only provided no element of compulsion to use said path existed. (Thin end of the wedge). I suspect that new/inexperienced cyclists would still dislike the environment they'd find themselves riding on as the lorries swoosh past on the adjoining road complete with huge air wash.
I believe a better case can be made, in many, many, instances, for using adjacent local lanes/roads (often including the 'old' A road before it was upgraded) as cycle routes, with appropriate traffic calming/speed enforcement if necessary, instead.
But the reality is that before we sort the trunk routes, and honestly who but the fit and furious will be using trunk routes on a bike, we need to sort the routes within our towns and cities. I believe the best way to do this is to simply accept we have a superb road network, perfectly safe to cycle on which is only made unpleasant by the speed and volume of the motor vehicles. The roads are not the problem. The way people drive is.
By way of practical demonstration I give you FNRttC.... We ride on roads out of London which would be near suicidal during the day. By riding them in the wee small hours the only hazard we face is each other. Low speed, low volume traffic = low risk.
I've ridden from Horsham to Worthing on the A24 at 03:00 am on a Sunday morning. A really enjoyable blast. Wouldn't even think of joining that road at 15:00. I even think twice about crossing it on the level. A264 between Crawley and Horsham; great early on a Saturday or Sunday morning and a great TT course. During the day? No thanks.
I repeat, the roads we have are fine, it is the traffic (speed and volume) that is the problem.