Two reasons I can think of wanting more weight on the rear are:
1) camber steer. Tires create lateral force in the direction they are cambered. This is why a coin turns left if you roll it and it falls to the left.
2) For a vehicle that does not steer the rear tires, your turning radius is a fixed line from your rear axle to the point where a similar line from the front wheel intersects. Yes, there's limits to this statement based on scrubbing with speed, but by reducing the weight on the front wheel, you're also putting a lot less of the lateral force to turn the vehicle on the front wheel. Let's not forget that the rider is able to pivot the front wheel relative to the vehicle, so if you're supplying a proportionately large amount of lateral force with the front wheel, the rider input has a significantly larger amount of effect on keeping the chassis steady. In my mind, that is why a bike is always smoother through a turn if you roll on the throttle and transfer weight to the rear of the bike; you've reduced the significance of any small steering inputs with the front wheel. This is also why it's so important for the rider to stay loose and relaxed.
Countersteering is how you get the bike to lean, lateral force from a cambered wheel is how the bike continues to turn once you're leaned. I don't think it's as much about front and rear contact patch size as it is about front and rear loading.
https://en.wikipedia.org/wiki/Camber_thrust
I also believe that your assumption of a static 50/50 weight distribution is wrong for a sport bike. From working with tadpole tricycles, I know they tend to perform well with 70/30 f/r static weight bias, and from looking at sporty motorcycles, I assume they carry the majority of their weight on the front wheel as during static conditions.