Instead, if you use one or two centralized exchanges, it will always come from those two bank accounts. This way, someone could link your outputs.
1] You send unlinked UTXO A to Binance
2] You cash out the amount to your bank account
3] You send unlinked UTXO B to Binanche
4] You cash out the amount to your bank account
Even though they were unlinked, by sending them to the same exchange and subsequently the same bank account, they can be linked.
Through Bisq, you could even sell one UTXO for fiat received via bank transfer, another for fiat received via Skrill, and another via 'cash in person'.
The above may not apply to those receiving cash in person, although engaging in this type of transaction is generally risky, and has a high risk of you getting scammed, so instead of losing your privacy, you may just lose your money.
Phoenix Wallet charges 3000 sats minimum when you deposit.
There are probably more LN wallets that can do this, but I don't know the rates for those by heart.