Point systems implemented by sanctioned racing groups, AWD adds points, weight, complexity, and money. Half the experience of tracking is finding a car easy and cheap enough to work in in the class you want to compete in; AWD gets crazy expensive to maintain and work on when tracking. When used in a higher or unrestricted time attack class like NASA TT1/2/U, they tend to place pretty high, if not podium. Weight is one of the worst things when trying to slim down an AWD car; you can't just take the transfer case, driveshaft, rear diff, etc etc out when putting the car on a diet and any decent aftermarket modifications to these tend to be expensive. When used in a higher or unrestricted time attack class like NASA TT1/2/U, they tend to place pretty high, if not podium. Anybody remember the Sierra Sierra Evo 8 back from 2010? That thing was a record breaker at nearly every event it ran at.
On the track AWD systems help with getting on the power earlier when coming out of the turn. Racing in the rain? Forget about it, no 2WD car is going to come out of a corner faster than an AWD, all things considered the same. Racing in the rain is rare though and doesn't happen enough to cause a concern.
So yes, AWD does help in turns and high speed stability. No your AWD system on your crossovers/SUVs will only help marginally and if a driver is dumb enough to think their CUV is going to go around a corner like Sienna because it has AWD then they deserve the consequences. No engineer is going to take or design an AWD for a Pilot/Atlas/Sienna/CX5 for the track no matter how much they market the "sportiness" of it.
IME every AWD system will cause the front to plow in a corner, no matter how good it is, even if it's just a small amount. There are way to mitigate the corner plow though which is why there's different torque biased systems and torque vectoring systems. Every manufacture does it different and the results can and will wildly vary.
Power and traction wins in a straight line, not drive type. Up to a certain power at least, then stuff starts breaking.