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 !
If they had only one feature to offer the service of an online bitcoin wallet then they couldn't survive by covering the fees.
But as we know they have other services like exchanges for usd/btc and ethereum recently (coinbase) so they take fees on every exchange.
Xapo besides exchange service they have also the bitcoin debit card which they take a fee as well.