The gearbox is going to be shifted out of park WHILE THE MECHANIC IS UNDER THE CAR.
If there is a subtle error in setting up the jack (e.g. if there is a slight gradient and the drive wheels are on the ground, so that the car is "resting" against the parking brake), shifting it into neutral could cause the car to move slightly as the longitudinal force is transferred from the parking brake to the wheel chocks / handbrake / jack / etc. If the situation is marginal, this could cause the car to fall off the jack and crush the mechanic.
It just seems like a recipe for (occasional, statistical) disaster.
I would never go under a jacked up car. Just use the jack to change the tyres that is it. Anything else I take it to the mechanic who will lift it with the proper machinery.
Oh indeed, most people wouldn't. I bet some people do though.
Especially if the car is broken down in the road (which is where cars usually break down), and there is no tow truck but someone has a jack (e.g. the basic jack for changing the tyre) and there is pressure to get the car off the road. It's inevitable that out of all the millions of cars and people, someone will be in
a hurry to jack it up using the spare tyre jack and not much else, climb under, put it in neutral without thinking of what will happen next, and get crushed.
The gearbox is going to be shifted out of park WHILE THE MECHANIC IS UNDER THE CAR.
If there is a subtle error in setting up the jack (e.g. if there is a slight gradient and the drive wheels are on the ground, so that the car is "resting" against the parking brake), shifting it into neutral could cause the car to move slightly as the longitudinal force is transferred from the parking brake to the wheel chocks / handbrake / jack / etc. If the situation is marginal, this could cause the car to fall off the jack and crush the mechanic.
It just seems like a recipe for (occasional, statistical) disaster.