You'd need a support crew at Cold Cotes to give you a 'road' CX bike, then another at the base of Whernside to swap onto the 'mountain' CX. Would a single support team have enough time to get past you and into position? Likewise from the Viaduct down to Horton.
That's the problem with it. If you're mid-field, it's risky whether the support crew have time and space to swap bikes, mount the discarded bike to the car, drive to the base of Whernside, unmount the bike and have it ready again.
It almost demands dangerous driving, stupid overtakes and inconsiderate parking as support crews slam their car into any available layby, rush around with bikes/wheels etc, then pull out and roar along to the next point, rushing past other cyclists and then trying to find a parking spot (or more usually, just abandoning the car any old how along the roadside in amongst 200 other cars).
They really need to ban bike changes altogether.