This is probably what exchanges see and it's very hard to convince them that you are not associated with illegal activities.
If a transaction has happened then it is impossible for the exchange to prove that that bitcoin has not changed hands in a completely legal and legitimate transaction. Look back far enough and every bitcoin in active circulation could be "tainted" by some algorithm or another. Every bank note in active circulation is probably the same. The problem here is not where the coins came from - the problem here is the centralized exchange making arbitrary, unprovable, and almost certainly false assumptions about OP's coins with zero retribution.
Oddly enough in the end using unorthodox methods like withdrawing from an exchange makes for better and also much cheaper mixing.
No, it doesn't. It provides the exchange with a 100% provable link between your coins and your KYCed identity and provides absolutely zero privacy whatsoever.