because mid is the sum of left and right, it makes duplicated sounds in the left and right cancel each other out. i think there is a very clear fix for this. left is the sum of mid and side, so unless sounds are duplicated in the mid and side, they won't cancel each other out. i think that mono sound systems should use left instead of mid so that stereo effects like detune and haas effect can still sound good in mono.
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i think it would be better for you to make it left channel only using panorama and then do the thing you wanted. this sounds really specialised. i feel like mono would be way better on both channels because I don't get why you would want to make your music on a single channel that is on the left (I'm not saying all of your music)
"duplicated sounds in the left and right cancel each other out" Only if they are in opposition of phase. If they phases match, they'll just amplify. But usually that's taken care of by a proper pan law.