I agree with your title for the most part but I do not think Battlefield 3 suppression was over-tuned but I do understand that people like different things just like how some people might like high FOV configurations; everyone likes something.
Something else I have noticed is that when some people play Battlefield 3 they use the guns incorrectly holding down the fire button at all engagement ranges and in all states (I am not saying this is you). Naturally my experience does not account for every person who plays but it gives me the feeling that those people are treating the game like a generic arena shooter and as such when their expectations don’t match the result they blame the tick rate, netcode, spread or suppression system, so they might feel more inclined to dislike suppression. Of course it could also be that some players just don’t like it and that’s fine, as expressed people have different preferences.
As to what I want I’d prefer the Battlefield 3 representation of suppression as the Battlefield 4 visual suppression rendering is often too subtle (at least to me) leading to an unintuitive shooting experience as it encourages you to shoot as you would when you are not suppressed increasing the likely hood of encountering additional suppressive penalties. This issue probably would not be too bad if the shot mechanics were based on the radius of the spread cone like in Battlefield 3 as this would provide a centre biased style shooting experience but in Battlefield 4 shot mechanics are based on the area of the spread cone which makes it that much more likely to miss by default.
So to summarise, the Battlefield 4 suppression system if applied to Battlefield 6 in my opinion would cause conflict with the kinaesthetic system and gun projectile mechanics as it would lead to people having to shoot first and note that they are missing in order to recognise that they are acutely suppressed, only when they are severely suppressed would a player be able to make a more informed decision. Battlefield 3 suppression is designed to give you the visual stimuli to adapt and overcome such that you know instantly to change your firing pattern and brace for additional recoil/drift penalties relative to the intensity of the effect both before and as you engage; it provides for multiple level of play and is a great attribute for building atmosphere and giving the impression that there is more destruction then there actually is (Try Battlefield 3 Metro and then try Battlefield 4 metro, same map different experience).
I think the developer should also look at Battlefield 3’s camera shake style because while Battlefield 6’s rendition looks acceptable it appears very robotic to me like you are a camera on wheels. Battlefield 3’s camera shake expresses more rotations that feature dynamic speed shifts to simulate the natural human frame wincing, jerking or lurching from nearby explosions. Again I feel this would add to the kinaesthetic design philosophy embedded in Battlefield 6.
https://www.youtube.com/watch?v=H4h9-AfoUPA&t=90s
*EDIT To add a URL as an example to my camera shake comment, the YouTube video I found is of someone demonstrating C4 in Battlefield 6 and Battlefield 3 but it's still relevant. I feel that the camera animations that occur from nearby explosions in Battlefield 3 helps to make the large explosions appear more powerful more credible; you can feel the force through your screen, you can feel the battle. Also in the Battlefield 3 clips do you notice the shorter throwing distance and slightly slower C4 animation to make it more situational and to help personify the item more as a serious tool rather than a toy. The soldier dialogue is great too!
P.S. Just putting this out there for any marketing staff that are reading this but I will purchase Battlefield 6 if Battlefield 3 style suppression is implemented even if it’s optional or voluntary.