(Pace): The racing driver is likely to drive faster but like for like is more likely to recover the situation.
So yes I am all for avoidance training but add the safeguard of feeling confident with the aircraft whatever it throws at you.
That does not mean the handling pilot will get away with it but he is more likely to than the untrained pilot.
The rather scarce and older findings I could find on the subject of racing drivers and accidents rather support the view that with (because of?) their superior wheel'n pedal skills, race drivers (or drivers trained in advanced car handling) tend to stretch their limits to an extent that rather results in a safety penalty [1]. One more recent study on the subject comes to the conclusion that a "focus on teaching drivers about self assessment and anticipation of risk, as opposed to teaching drivers how to master driving at the limits of tire adhesion" is considerably more promising concerning safety outcomes [2].
IMHO same goes for flying; the problem is arguably not so much what the aircraft may "throw at you" by itself, but rather what the pilot
makes or lets the aircraft throw at him/her, and while the handling pilot is probably indeed more likely to get away with an identical "it" compared to an untrained pilot, taking care to stay out of trouble from the outset seems to be the better choice for accident prevention.
[1] e.g., A.F. Williams, B.F. O'Neill (1974), On-the-road driving records of licensed race drivers, Accident Analysis and Prevention, 3(4), p. 263–270.
[2] S. Washington, R.J. Cole, S. B. Herbel (2011), European advanced driver training programs: Reasons for optimism, IATTS Research, 34, p. 72-79