Looking at the two popular web wallets as an example. Blockchain.info and Coinbase. Blockchain.info is a client-side wallet implemented in JS Keys are encrypted client-side and encrypted keys stored in the server. There are good good benefits there because if blockchain.info is hacked, your keys are still with you and not compromised (Different story if the server starts serving malicious JS though)

The server-side wallet approach means that if their hot wallets gets hacked, all the funds will be gone.