It's multifactorial, of course. I think anyone should be able to cycle on any road (well, with the sensible exceptions) without fear of aggression and endangerment from other users. The reality though, as we know, is that there's close to no enforcement of the law. There seems little political appetite to tackle that.
That aside, fast, busy roads, are not pleasant places to cycle. There's a differential in speed, you're chomping on exhaust fumes, usually confined to the worse bit of the road by vehicles for whom a wide pass is the exception rather than the rule. I think I can see why people don't leap at the prospect.
As mentioned, I bought a bike after a long hiatus from cycling to get to the pool and back (a five-minute scoot), it was only the enticement of a traffic-free route that got to ride into central London. I know a fair number of Europeans who cycle in their home country but view even London cycling as the domain of the mad.
Being able to get from (a) to (b) without these challenges makes it possible. You probably wouldn't encourage walking by getting rid of the pavements and telling pedestrians they're better off walking down the side of the road.