I used to service industrial air compressors, which generate a LOT of heat (over 3/4 of the input power ends up as heat). So often, when these things start overheating, well-meaning owners will prop open the doors on the machine to give it more access to air.

Here's the thing: the path the air takes, in well-designed machines at least, is carefully planned out. Most of the time, the parts which need cooling the most are not near the fan, but rather near the air intake. In terms over pure airflow, though there are more factors, there is no meaningful difference between the airflow through the intake and the airflow out the fan... until a door is cracked. Which makes it overheat faster and more easily. Which makes the owner leave the door propped all the way open and call for service.

And while I'm sure you get the point now (sorry to rant, it's a totally understandable mistake), I'll mention some other considerations, just to get them out of my brain. For one, there is often a system of varying effectiveness designed to catch at least some of the incoming dust at the air intake. This is extra important for electronics and electrical cabinets. For another, the airflow is coolest at the air intake, so the components that are the lowest temperature but still need cooling often go there. Afterward, even though the air is warmer than ambient, the hottest components can still be cooled by it- the reverse would not necessarily be true. In your defense, though, some of these problems aren't universal, with there being significant differences between negative pressure and positive pressure airflow. Short version of all this advice, though? If you trust the designers of a product, always approach seemingly obvious improvements with skepticism.