The whole point of Cyclecraft, Effective Cycling and the national schemes that take these manuals as their foundation, was to find the safest way (not the fastest, most convenient or most law-abiding way) to cycle. The whole reason we ride in the road is because it's the safest place to ride. That's why we who have learned to ride using these cycling safety schemes don't advocate pedestrian-style turns - because they're less safe.
In cycling, what looks safest often isn't. Walking a bike across lanes of traffic increases risk. We are far safer negotiating a turn using the standard rules and infrastructure of the road that have been developed over 120+ years, than we are when we make up our own rules whose prime motivation is to calm unfounded fears about the dangers of operating a bicycle in the street.
The road isn't anywhere near as dangerous as some cyclists make it out to be. If it were, I would have been knocked off my bike at least once in my 40 years and 20,000+ miles of road cycling.