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There are much more complex cooling setups that can be achieved that utilise outward-blowing fans though, but a single fan can't will cool _you_ faster if it is blowing onto you.
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Just to add, for computer cases, you want it to be a high pressure zone because intake fans generally have filters in front to catch the dust before it gets into the case. Negative pressure means dust gets sucked in from the cracks.
Same applies for house fans -- you want the intake fan to be slightly stronger than the exhaust fan. Else the negative pressure will draw outside air in through cracks and all the fun smells that come from those places. (I have a combination energy recovery ventilator/HEPA filter that has has a restriction filter on its exhaust for this reason. Else it would just suck crappy air in from the basement instead of fresh…
Cooling the entire house is an expensive proposition if you're just trying to get to sleep in one room.
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Also while extremely trivial here, higher pressure air has a higher capacity to transfer heat.
While this is technically true, the difference is very minor at the typical pressure ranges being used. The highest performing PC fans create about 10mmH2O pressure while typically you can expect about 1mmH2O pressure compared to 10mH2O of the atmosphere. This translates to densening of the atmosphere around components by 0.1% or 0.01%, respectively. Correct placement and design is by orders of magnitude more importa…
I'm guessing you've never worked with a Delta fan. Those things produce enough pressure to literally suspend themselves in mid-air.
Open your bedroom windows on a cool spring/summer night. On the opposite end of the house, put a fan in a window blowing outwards. This cools the entire house, giving your bedroom the freshest air. In the morning, close all the windows. This leaves the house cooled and drastically reduces your A/C usage.
Blowing inward doesn't have the same effect of pulling air through the whole house.
Recently, I bought a whole-house attic fan. Now, I open a window on the upwind side of the house and turn on the attic fan, which is enough to suck a toupee off someone's head. The attic fan both circulates cooler air and also clears out the hot air built up in the attic, which helps a lot.
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Fans -> cool human via wind-chill [1] Air conditioning -> cool human by cooling environment [1] https://en.wikipedia.org/wiki/Wind_chill
You can also use fans to cool the environment, trading hot inside air for cooler outside air. For example https://en.wikipedia.org/wiki/Whole-house_fan