If the cyclists are strung out in a long unbroken line then you might not have long enough to overtake and pull in before the next corner, whereas if they road in clusters of riders then you would have spaces into which to hop without causing any danger for anyone.
Leaving "car-sized spaces" is the worst possible thing that any club can do. Car overtakes, slots into gap and it's now sandwiched between two groups unable to overtake further. Runs the risk of cyclists behind increasing speed (descent for example) and trying to re-overtake the car or being dangerously close to it, usually through no fault of their own.
The problem is that drivers don't usually understand the dynamics of a club run - why riders are 2-abreast, why/when riders might choose to single out or take primary or why a group might stretch out or bunch up briefly (on descents and climbs).
Having cyclists pass a test is just another one of those false reasoning arguments that some motorists use. That combined with "road tax".