"exchange would be able to track all further transactions you make" is just false. They will see the withdrawal tx and assume this is my address. The next tx from this address can be me paying for drugs and sluts, or moving to my other address, or both (I know how to pay with no change). They cannot prove beyond reasonable doubt whose those following UTXOs are. Even the first address can be someone else's if I donate or repay a debt. Buying someone else's "KYC" coins p2p to turn them into "non-KYC" is absurd if everything is traceable. If I spend them to finance terrorism the other guy must be jailed regardless by that logic.
What about pegging into Liquid to evade chain analysis?
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Yes, even better. Bitcoin in three forms - onchain, lightning, liquid - morphing into one another like this: https://medium.com/@goryachev/liquid-rebalancing-of-lightning-channels-2dadf4b2397a
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