That may not be a cheap fan cost-wise, but as you found out it's completely inadequate. The fan shroud is just a cookie sheet, not a piece that was designed for air flow. And the fan itself is only rated for half of what you'd need to cool that engine, if that.
Buying an expensive aftermarket fan does not guarantee success. You need to make sure it can put out enough CFM for your application, and it has to be designed to work with its shroud to flow air. The Ford Contour electric fan set up I run costs significantly less than that DeRale, and flows twice as much air.
Your RPM example is exactly why mechanical fans are inefficient. The fan has to do the most work at idle, when a mechanical fan is turning the slowest. At higher engine rpm's the car is MOVING, which means your airflow is coming from the speed of the car, not the fan. You don't even need the fan to be spinning at all once you're doing 25mph or more. The electric fan always spinning the same speed is an advantage, it can flow the most air when the engine is at idle and the car is sitting still, which is exactly when you need the fan to be doing the most work.
And yes, I am very familiar with how much air a mechanical fan can move. Which is why I picked an electric fan that can move just as much. If you've ever seen a Contour fan set up running at high speed, you'd know it moves just as much, if not more, than the mechanical fans these cars came with. Especially if the engine is just idling.
I don't need to do any research on cooling a dirt car, there are electric fans more than capable of cooling those engines. But as you said, the class of racing you're talking about doesn't run alternators. An electric fan that would cool those engines needs to be supplied with 40+ amps of power to deliver their rated CFM. This just goes back to the basic mistakes people make when choosing electric fans- they don't pick a fan with enough CFM, they don't wire it with the heavy duty wiring and relays needed to supply the power they need, and they don't run a power source capable of feeding the right amount of power to the fans when they're running.
I have no issues cooling my 400+ hp, all iron 340 with the electric fans I run. They never even come on when my car is moving more than 25 mph, and they've cooled it just fine when it was 110° out and I was stuck in traffic. That's a harder ask than anything a dirt car with 400 hp requires.