So an air-cooled engine has no need for a radiator, a water pump, coolant, hoses or any other associated parts a liquid-cooled engine has. But is this actually a good thing?
The short answer: Sometimes.
Obviously, and air-cooled engine doesn't have coolant leakage problems and won't ever require things like the water pump or radiator to be replaced, which can be a great thing. Typically, they're lighter than liquid-cooled engines, too, because they have fewer parts.
Air-cooled engines also warm up a lot faster than liquid-cooled engines and don't have any risk of the coolant freezing, which is beneficial if you're operating the vehicle in extremely cold temperatures.
But there are some considerable drawbacks, too. For starters, air-cooled engines are more likely to overheat. Yeah, that's a bummer. They can also be more expensive to build and the large fans used to cool the engine can take away a lot of power.
This doesn't mean that air-cooled engines are bad or ineffective. In fact, for motorcycles, recreational vehicles and certain aircraft the air-cooled engine works extremely well. But on cars, the common consensus is that the drawbacks outweigh the benefits.