Yeah; even with the lancool you’re unlikely to see any real benefit. You’d need bottom fans that actually attach to the bottom to overcome the resistance. Maybe you pull some air from the front-bottom intake that’d end up feeding the PSU, but not much.
Fan mounted push vs pull makes very little difference. Tested on radiators the temperature difference was 1.0-1.25c at 800rpm and even less at higher speed. Radiator is way more restrictive than case venting.
Taking what you posted literally, when you said "bottom fans that actually attach to the bottom" would put fans on outside of case meaning bottom of fans would be as low as bottom of case feet, maybe even lower as most feet are less than 25mm tall
Cooler air sinks, warmer air rises, as long as you have 1+ inch gap you shouldnt have an issue
Scientifically you are correct. It is what creates stack (chimney) effect in buildings and chimneys. But in computer cases even the very slightest external force (fan at lowest speed is many times needed effect) over-powers any air movement generated by air temp in our cases.
A good example of how little pressure our computer fans make, I calculated atmospheric pressure at 30 feet above sea level. There is a 11.013 mm H20 less pressure 30 feet above sea level than at sea leve.
Simple math shows that is 3.671 mm H2O less 10 feet above sea level than at sea level.
Or 1.863 mm H2O less 5 feet above sea level than at sea level.
That is about 1.836 mm H2O less pressure on our chest than on our feet.
The fans we use in our systems rarely have static pressure rating as high as 1.836 mm H2O .. and that is at full speed .. which most of us never use. At lower speeds their pressure differential is even less.