Because from 2,602 to 370 looks like an enormous reduction for a falling object that is supposed to increase speed as it falls
A falling object increases speed only up to the point at which air resistance (which increases with the square of speed) balances the force of gravity (which remains constant). This balance point is called terminal velocity, and varies mostly with the mass and cross-sectional area of the falling object, and the density of the surrounding air.
That last part, the air density, is the most important factor. At 28km altitude, the air density is only about 2% of sea level. During that descent, air resistance increases by a factor of 50, and your speed falls accordingly.
Almost all of this reduction in speed would occur with or without the air brakes, the same way it does for any crewed-capsule reentry. The air brakes, when deployed, slightly increase the cross-section of the stage, and thus the air resistance, which lowers the terminal velocity.
The other function of the air brakes is to improve the stability of the descending stage. Objects moving ballistically through air tend to orient themselves with the denser end forward and the air-draggy end backwards -- like a throwing dart, with a heavy head at one end and a finned tail at the other. If the stage starts to turn in flight for any reason, the extra drag on the extended air brakes tends to straighten it back out.