Karts do lockup when braking, but it is not to slow the kart more quickly, it is to pitch the kart into the corner before you even get there.
For Itpro's question, the tyre doesn't have to know. Study some tyre data and watch the grip increase with slip angle until (and especially with radials but less so cross-plys) grip reaches a peak and falls off a cliff. The same principal applies to the tyre longitudinally.
As an extreme example, if you were travelling 20kph and were braking hard enough to reduce wheel speed by 20kph, your wheels would be locked and you'll have little braking force. Now travel at 100kph and reduce wheel speed by 20kph and you may find (depending on the tyre, that you're at peak braking force. It's no different in concept to the slip angle above; you're simply putting a certain level of deformation into the tyre.
Liam's data shows the limitations of drivers and the benefits of modern ABS. Firstly, the driver can only control the braking force as applied to all four wheels (ABS can control the force to each)) Secondly, the ABS can operate much closer to the limit.
Karter's being quick in cars has little to do with braking (or any of the other driving skills). Karter's biggest advantage is most often racecraft and their wealth of racing experience. Also, karts are far more rapid than cars until you get to the high downforce high powered stuff so karters to be a lot more at ease and feel a lot less rushed.
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