Having played with a friend's system... I don't find that 3x1200rpm fans are particularly quieter than 1x1800rpm fan at full blow. It's a
different sound, but if you look at the reviews the difference between a good air cooler and a basic AIO is 1-2 dB. You can get the top-end AIOs, but I don't want to pay more for the cooler than I did for the CPU. I'm also wearing headphones while gaming, so it's largely irrelevant as both are silent to my ears at idle and at full blow the GPU fans are screaming anyhow. (You could always AIO the GPU too, but that's a larger project than I'm comfortable with and quite warranty-voiding)
I don't want to say "don't do it", but for a majority of people I think AIOs are an aesthetic choice rather than a performance one. Unless you've got an Intel i9 or something that really needs it.
Eg: Here you can see the Peerless Assassin being quieter at load than any of the AIOs they tested it against. The AIOs were quieter only at rest, but I can't hear my fans at rest anyhow.
Shockingly cool and quiet, less than $40!
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