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The statement indicating that "Fan speed increases with engine warming" is not a cause for fan clutch replacement because it describes normal operational behavior of a fan clutch system. As the engine temperature rises, it should increase the thermal response of the viscous fluid within the clutch, causing the fan to engage more fully and match the increased cooling needs of the engine. This is a typical function of a fan clutch and reflects its design to help maintain proper engine temperatures.

On the other hand, the other options describe conditions that indicate a malfunction or failure within the clutch mechanism. Oil film on the back of the clutch suggests a possible leak or failure of the internal seals, which could lead to proper engagement issues. No viscous drag indicates that the fluid within the clutch is likely insufficient to create the hydraulic force needed to engage the fan when necessary. Lastly, if the fan stops spinning too quickly after the engine shuts down, it may suggest that the clutch is not retaining enough fluid pressure or that the internal components are compromised, impairing its ability to function as intended. Therefore, only option C reflects the expected functioning of a fan clutch rather than a reason for its replacement.