Why should you not apply the clutch when driving on a long, steep downhill slope?

Your answer is correct. When you apply the clutch while going downhill, the engine is disconnected from the wheels. This means you lose the braking effect of the engine, so only the brakes are used to slow down the vehicle. Relying only on the brakes can cause them to overheat and wear out quickly, especially on a long, steep descent. That’s why you should stay in gear and use engine braking to help control your speed and reduce brake wear.