The Cessna C 172 parking brake is not very well designed.
Over time the cables stretch and uneven pressure is applied to each side as well as system friction can cause the brakes to not fully release. For that reason I teach that the system never be used.
Trusting the Cessna Mickey Mouse parking brake to hold during runup is IMO the height of foolishness and any student that is not capable of holding the brakes while performing the appropriate checks is IMO not fit to hold a licence. Leaving the parking brake on after the flight will warp the brake discs.
My 02 cents
Hold the brakes with your feet when the engine is running and use chocks when the aircraft is unattended.