Improving that exhaust fan can help a lot,
along with ducting from it to the CPU cooler fin stack.
Yep, although it highly depends on the case too. My last case (2011-2020) had a closed front with only the bottom half on the sides of the front being open with slits.
No mesh anywhere and only a 120mm rear exhaust. PSU in the bottom.
The 2x 140mm Be Quiet Silent Wings barely helped. The CPU fan itself had a big impact but got a bit stuck after heating up.
The rear fan's RPM had as much impact as the CPU fan, as soon as the CPU fan was above 60% speed.
Now I have a big Fractal Meshify S2 with a mesh bottom, mesh front mesh top and a few slits here and there at the rear that allow some air output around the GPU.
To be honest, none of the 6 fans in that case have any really impact apart from the cpu fan.
The air is just swooshing around however it wants without any chance of getting some directional flow.
I even ducted the cpu cooler and the rear fan: no difference apart from more sound from the moving air.
Putting an exhaust fan above the cpu was worse than the free mesh up until 70% of the fan speed (silent wing 3, 120mm, 70% = ca. 900 RPM).
Also all the air cooler are very similar. It seems that it's simply about the raw surface area and the RPM of the fan (and its effeciency).
The fan determines the noise, the width of the gaps between the fins determines if it works great for not too high loads and low RPMs or for high loads with high RPMs.
So if its not about visual aesthetics, just buy the biggest CPU cooler with not too tightly packaged fins and with a good fan. Or rather a fan that doesn't completely suck.
Or an even cheaper cooler with a shitty fan and replace that fan