If you think that cycle experience makes for better drivers, then I suggest you think on London's cabbies, many of whom spent a lot of time on a PTW doing the knowledge. Do you think that made them more empathic?
As a former motorcycle courier, I shared the road with C90-mounted knowledge boys for some years. London cabbies do not have the best reputation, but I'm not sure BM's example works as an effective dismissal of the principle.
I'm pretty sure that experience dealing with the differing dynamic characteristics (speed, size, handling, visibility, braking performance and similar) of several different vehicle types does improve one's ability to make some of the judgements necessary in today's traffic.
My daughter (who learned to drive last year after a childhood as a keen cyclist) was surprised how much she gained in terms of cycling from steering a car around our lanes and local towns.
Similarly, I feel my decidecly modest skills behind wheel or handlebar are less crap than they might be through years of experience with lorries, motorcycles, bicycles, cars and tractors.
Just as I know many drivers who don't 'get' bicycles because they are strangers to them, so I know one or two cyclists who fail to grasp the movement and speed of cars because they have only ever been a passenger in one. That's not a criticism and I'm sure it's not universal.
But I think there is much to be gained from having a modicum of experience or qualification in piloting a range of vehicles through our streets.