Yes it does. Your trade counterparty will always know something about you.
The bank or payment app won't know the payment was for a bitcoin trade unless your counterparty volunteers that information.
Even if they do that, that would only reveal the information related to that specific trade alone.
In order to get all your trades, LE would have to somehow track every possible trade counterparty and pressure them to reveal the data.
Compare that with just using a SINGLE counterparty!
Yes, cash-in-mail or gift cards are theoretically better. But we shouldn't let the perfect be the enemy of good. Instant small fiat payments are very liquid on p2p markets and very convenient. They also just pass as simple transactions between friends.