Prove it. Which mechanical fan? Which electric fan? Are the blades designed the same? What speed is the fan spinning at? How much surface area? What fan controller? Which fan clutch? You can't show that every mechanical fan is more efficient than every electric fan, because it's not true.
The biggest advantage to an electric fan is the accuracy with which you can control it. That has a huge effect on efficiency, you only run the fan when you need it. Mechanical fans are stuck with a fluid or thermostatic coupling of one type or another, and they simply aren't that accurate. Which means at some point you're spinning the fan when you don't need it, or not spinning it when it might help. Further, the fan blades aren't spinning at a constant speed, which has a huge effect on fan blade design and air flow.
There's A LOT more to it than the power required to spin the alternator and the electric efficiency of the fan. Can a mechanical fan be more efficient than an electric one? Sure. Can an electric fan be more efficient than a mechanical fan? Yup. It depends on the fans being compared and how they're being controlled, and there is a wide range of quality for both electric fans and fan controllers.
And really, efficiency isn't the most important part. Effectiveness is, and with a good fan controller an electric fan can be just as, if not more, effective than a mechanical one.
