Many of the online wallets services (like coinbase, blockchain, xapo, etc.,) having their own exchanges and they'll have some fees. OR if wallet doesn't have its own exchange (blockchain.info) there will be some ads on that website. I think this is the way that they're live (?).
I think their income not come from fees but from other we never know as we know if the fee transaction is for the miner.
definitely not the fees,when you input a fees all the fees that you're just input is not being cut off by the online wallet,it's all to pay the miner fee for the transaction,for proof,if you use blockchain,copy the transaction id (tx) and then explore it in another blockchain explorer and then the fee will remain the same as you input before