[COD] Is playing on a high sensitivity (on console) overrated?

Ever since I started playing CoD back in Black Ops 1 I was always looking for ways to improve, and one of the first things I looked at was the control setup. The advice I always heard, and that I still hear to this day, in almost every CoD when it comes to sensitvity is: "Higher is better, the higher the sensitivity you can play on the better."

So as you can expect in BO1 I tried gradually increasing my sensitivity over months of play until I eventually got to 7 sensitivity (highest was like 10 or 11 I think). And I could play on 7, I could put up pretty decent scores on 7, I was "good" at playing on a high sensitivity like everyone said I should be... It wasn't until I heard Sandy Ravage, who at the time was someone I looked up to as one of the "best" pubstompers, say he typically played on "2 or 3 sensitivity" that I started to question if running a high sensitivity was really always the best option. I mean if this guy was putting up 10 K/D games consistently while playing on a low sensitivity then there must be more to it.

So then I started going in the opposite direction, I started lowering my sensitivity and trying out different ones for a few days until I eventually settled on 4. What I found was that while I was able to aim and play just fine on 7 sensitivity I was actually a much much better player on 4, my shot became so accurate that I started hearing players accuse me of "aimbotting". I didn't even realise it until I lowered my sensitivity but mid-long range engagements are a cake-walk on low sensitivity.

Sure, if someone snuck up behind me I wouldn't be able to 180 as fast as I could on a high sensitivity but honestly how often do you find yourself having to 180 to kill someone vs how often do you wish you had better accuracy at range? I found I could play the game "smart" and learn the maps/spawns to minimise the chance of someone coming behind me which eliminated the need for playing on a super high sensitivity. My close range engagements surprisingly didn't suffer either, maybe I'm a few milliseconds slower to get on target than the other guy but once I get on target I never miss a shot and I never "overshoot" and have to re-correct me aim -- which is something I notice a lot of high sensitivity players doing a lot when I spectate them in SnD.

To this day I still tend to stick to the low/mid-range sensitivities (I play on 5 in the new MW) and I find that I'm a much better player because of it. Playing on a high sensitivity while it has it's benefits leaves you with less margin for error, and not just human error either, analogue sticks aren't perfect and especially over time they tend to not be 100% accurate.

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Sorry for the long post, I just wanted to layout my thoughts on it before I asked the question:

Do you think playing on a "high sensitivity" is overrated? Rather, is it really necessary to play on a high sensitivity to be a "good player"?