Because it's a proven way to get the trailer back under control.
Great, link to the carefully controlled engineering tests that prove the maximum possible cornering speed is with trailer brakes on. What engineering principle determines the optimum braking force? Sometimes it is helpful to consider extreme examples to understand what happens between those limits.
Case 1: Trailer tires are rotating freely with no braking at all. All of the force generated by the skidding tires is applied parallel to the axles pushing the trailer back into position with the maximum available force.
Case 2: Brakes locked, tires skidding like a hockey puck. the force generated by the tires is parallel to the skid marks. The Component of force parallel to the axle is small at small angles, increasing to 100% at 90 degrees of trailer rotation.
My guess is some people in this situation recovered despite applying the brakes and credited the recovery to their lightning fast reflexes.
There is another condition I’ll call Dynamic instability, where the trailer can start swinging side to side. This can happen on a straight dry road with maximum traction. Braking the trailer tires helps this condition by REDUCING the lateral force and speed.
