[...]
Doesn't that require you to already have a channel with the amount you want to mix, so that you can immediately exchange LN-BTC for BTC? Also, what about the time? It plays a big role when it comes to privacy. If a chain analysis company routed a 0.16 BTC payment it could be far nearer to the new address. (That received money few seconds/minutes later)
You don't need a single channel; in fact it would even better if your channels are smaller than the mixed amount, because then it's guaranteed that the payment
has to be split in multiple smaller ones.
But in general anything a little bit larger usually takes multiple different paths to its destination.
As I said, when it comes to correlating input / output sizes, you can break that by choosing random amounts that are sent to the LN wallet in different time intervals (network topology also changes over time) and sent back out at different time intervals and in different sizes than what 'comes into' the LN wallet as well.