Closed-source wallets may charge a fee every time a customer makes a transaction, and this fee is so small that it goes unnoticed.
Additional fees would just go straight to the miners, extra output for their hidden fee will
stick out like a sore thumb as Charles-Tim mentioned.
Plus it wouldn't be practical since small amounts can be troublesome to consolidate.
You're probably thinking of custodial wallets which is similar to what OP already pointed out.