What would happen if a pilot were to use the parking brakes after touchdown in order to slow down?
This question appears to have an implicit assumption: that the parking brake would provide more deceleration than is available from normal braking. This is not generally the case.

A much greater worry for pilots than insufficient braking is actually excessive braking - to the point that the wheel locks up and skids. A skidding tire provides much less braking than a rolling one, and also quickly acquires a flat spot. Even on dry pavement, maximum braking would require an anti-skid system to remain effective; consider a 757 and a Mig-29, each of which blew out their tires when their anti-skid systems failed.

Note also that in small planes without complex braking systems, the parking brake merely maintains the pressure that is in the brake lines at the time it's applied. The parking brake would have no effect if the pilot were not already on the brakes, and would not be able to add any additional braking than the pilot could otherwise apply.