Just consider that, for an instant while overtaking, you are on the wrong side of the road, with one hand on the steering wheel, in neutral and with no feet available for braking.
Overtaking should be attempted only with the utmost caution!
Only if you are changing gear. But why would you do that?
As Dave W says, overtaking is an art. Part of that art is making the acceleration run and gearchange before you pull out. In any decent supercar, you are actually backing off the throttle as you go past to match roadspeed as you pull in ahead.
But we are agreed on the importance of caution.