Ask anyone that's been in automotive cooling or climate control. Well known fact.
Well anyone in the thermodynamics, aeronautics or physics industries would tell you you're wrong. It's not an absolute. If it was, Hellcat's wouldn't run electric fans. And yet, they do. Think it's cheaper to design an electric fan system, program the controls, and provide the electrical capacity than it is to bolt on a mechanical fan? Well, it's not. So it's not because of the production costs.
Any time a mechanical fan spins that an electric fan wouldn't is 100% waste. Sure, when the mechanical fan and electric fan are both spinning you might have an advantage in efficiency. But you might not, because the speed at which the mechanical fan is spinning might not be it's most efficient speed. And then there's the fact that you're always spinning the alternator already. Yes, there's more resistance when the alternator is at max output, but now you have to know the average resistance and efficiency of the alternator when the fan is running compared to when it's not. Then consider that the electric fans can be set to control the engine temperature to a narrower window, where the engine itself is more efficient.
And we haven't even gotten to running multiple electric fans to improve surface area coverage. Sure, there's a penalty for having two motors, but now they can be smaller and draw less, so less drag from the alternator etc.
And I could waste my time picking a specific example and doing a thermodynamic efficiency analysis on it, because I've done them before. But it still wouldn't tell you which one actually worked better on the road. I can though, I ran multiple different mechanical fans on my Duster. My dual electric fan set up from a Ford Contour works better than all of them. Is it more efficient? Don't care. My car has never gotten hotter than 205*. If it did, the high speed on my fans would kick in. They never have, and I've driven in traffic when it's 110* out. It was much harder on me than my car (no A/C).
Believe what/who you want. In some cases a mechanical fan will work great, and they're stupid simple and easy. But in some applications an electric fan is a much better choice. Just the facts.