The whole proposal has its pros and cons.
Consider the dual carriageway in principle: subject of this thread. Surprisingly, perhaps (well not to some people), there are a few instances where I feel safer on the D/C than on a fast single carriageway.
Consider
this locality which lies across one of my favourite leisure rides. What I often want to do, is cross the map area west-to-east, from Shipley to the west, to West Grinstead and Partridge Green to the east. On roads, only. Now I have two alternatives without a long detour: north and along the A272 S/C (at top), or southeast to Dial Post, about a mile along the A24 D/C, then east along the B road to W.Grinstead. There are no suitable routes on 'yellow' roads entirely, as you can see.
The A272 has a lot of traffic, a bad accident record, and is just at that width that you cannot be comfortably overtaken by a car in the face of an oncoming car. Which of course I am fully aware of, albeit some motorists aren't.
Can you wonder that, more often than not, I opt for the A24 D/C rather than the A272? The A24 has
no cycle path on that stretch. It is hairy, true, 70mph traffic throughout (well, more like 80-90mph in reality), but
provided drivers see you they have room to pull out and give you plenty of room. Provided they see you. But surely that's paramount to safety on any road. You can be hit on a narrow country lane just as easily as on a D/C.
I don't consider taking primary position on lane 1. Not trying to be a maniac! Just a nice steady position not too far from the left hand lane edge. As I see serious roadies, guys on training runs, doing it.
Maybe some folks are right, this sort of riding is not for the fainthearted. Question: how long do you have to have been a cyclist, to graduate from 'fainthearted' status. I've been a cyclist for nearly 50 years. Maybe that's too long! But I'm sure I was negotiating D/Cs in my twenties. Plenty of them.
Having said all this, it's not a pleasant part of the ride, of course. I can put up with it for one or two miles. I wouldn't care to do twenty.
At the end of the D/C stretch, I have, of course, a right turn, for which there is a right-hand slip road. Another trial! Usually I can time it so that I get across safely. But if I'm forced to stop on the LH side, wait for a gap, I don't consider it a humiliation - just a realistic way of getting across fast dense traffic at a pinch.
As I said, no cycle path on this road, either way. So I have no option. Other D/Cs in the area do have cycle paths, notably the A23 London-Brighton trunk, a few miles to the east. The quality of the cycle track is very variable. Some parts are as bad as Jacomus' video. Others places we have a reasonably straight and clean segregated track, wide enough for light cycle traffic, few pedestrians, quite adequate in my view. I use it. Yet further stretches are in fact parts of the abandoned old A23 (single carriageway) which have been left in place, downgraded to 'B' road, when the new D/C was cut through a green field route. The stretch through the villages of Sayers Common and Albourne, for example. These sections may not have been, environmentally, the best option. But they are perfect as cycle routes. Full-width roads carrying only light, local motor traffic. And cyclists. But of course, you have to be very lucky if your local trunk road has one of these.