Heatsinks apparently offer a perk over using an AIO

[arknor]

apparently grounding CPU heatsink has always been a thing?

I found this post from all the way back in 2005
according to the poster AMD had a white paper saying it reduces EMI by -4db, but since the post is so old the white papers link is dead.
apparently it turns the heatsink into an EMI shield

Reduced my PC's EMI emissions : What Great Sound Quality....

This has to be the best tweak i have ever done. After following AMDs suggestions on reducing EMI(from a pdf whitepaper),I did the following. 1) Connected a Wire between the heatsink fins and Ground.That is ground of t he power connectors. AMD says this reduces EMI by 4db!! 2)Connected a...

www.head-fi.org

Googles AI even backs up the claim

Grounding a CPU heatsink helps to reduce emissions and ensure that the heatsink shields the integrated circuit (IC) from high-frequency (HF). Here are some reasons why grounding a heatsink is important:

• Reduces radiated EMI
  Grounding the heatsink returns common-mode displacement current to the reference plane, which reduces radiated EMI.
  
  
  
• Prevents the heatsink from acting as an antenna
  If left floating, a heatsink can act like a large dipole antenna and radiate strongly.
  
  
  
• Reduces voltage difference
  Grounding the heatsink to the printed circuit board (PCB) ground-reference-plane (GRP) reduces the voltage difference between the heatsink and the ground reference plane.

Some ways to ground a heatsink include:

• Using a heatsink with a conductive finish
• Using a smaller grounded heatsink
• Using a grounded thermal washer between the heatsink and the component

A heat sink is a component that absorbs and disperses heat generated by electronic components. It's typically made of a thermally conductive material, such as aluminum or copper.

How come I've never heard of anyone doing it?

further investigation even reveals the gas lifts in office chairs have been known to output enough EMI to make a monitor blink

Display intermittently blanking, flickering or losing video signal – DisplayLink Support

support.displaylink.com

Surprisingly, we have also seen this issue connected to gas lift office chairs. When people stand or sit on gas lift chairs, they can generate an EMI spike which is picked up on the video cables, causing a loss of sync. If you have users complaining about displays randomly flickering it could actually be connected to people sitting on gas lift chairs. Again swapping video cables, especially for ones with magnetic ferrite ring on the cable, can eliminate this problem. There is even a white paper about this issue.

So why aren't we all wiring our heatsinks to the case or ground pin on the mobo?

 

[Rroff]

Even with a window, etc. the case itself should protect from most external noise albeit some don't have much metal aside from the motherboard tray. Most internal sources of noise probably already reduced in impact by common mode rejection where appropriate.