More surface contact != More traction.
Grip in a motorcycle is only really limited by gravity. That's still far better than most cars. The average motorcycle (or bicycle, for that matter) will have little problem hitting 35 degrees lean and therefore produce lateral G forces exceeding that of a typical car.
Same is true for deceleration, the average bike is going to be able to slow down as fast or faster than the average car, even if you just let ABS takeover.
Motorcycles don't have any disadvantage in grip unless you're comparing them to the supercars that have significant downforce.
It really does come down to practice. The machine itself is more than capable. Even a cheap entry level motorcycle is eminently more capable in terms of braking and corner than many sports cars. The cool thing about have two tires, is that you don't need a super fancy suspension setup to be able to corner fast, you just need good tires.