There are many online wallets like Xapo and Coinbase that do not charge any transaction fees or they pay that fees by themselves. I want to know that how would they profit from paying for their user's transaction fees ?
If no fees is charged then the transaction take a much long time or even might get cancelled !
Ones like blockchain.info make money from ads though it wouldn't surprise me if they start charging fees at some point in the future. They've had big investments from companies so they'll probably start wanting to see their money back at some point and its got to come from somewhere.