Drum-in-hat parking brake linings have higher coefficient of friction than service brake linings to

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The key idea is that a parking brake must hold the vehicle in place, not slow it down while it’s moving. When you engage the parking brake, the wheels are effectively stationary, so you rely on static friction between the brake lining and the drum to prevent slipping. Static friction can be higher than the friction encountered during normal braking, so using lining with a higher coefficient of friction helps ensure the vehicle won’t roll on grades or under load, even after long periods of parking or on an incline.

This is why drum-in-hat parking brake linings are chosen to have a higher friction coefficient: to provide a secure hold for a parked vehicle. The other options don’t address holding a stopped vehicle as the primary purpose—fuel efficiency, steering response, and brake fade are not the main reasons for the higher friction in the parking brake.