I feel the issue is not online wallets, but insecure online wallets. How is an online wallet without 2 factor authentication even expected to work well and be secure?
It is also a matter of trust. How do you know that the owner won't disappear with all of the bitcoins of the users?
Then, the security is also a concern. It is not possible to know whether the system (no matter how many authentication factors it uses) is secure or not, well, until it is hacked (I think Sony though that their system was secure until the hack too). Next is the account security. Two factor authentication is a must, and all banks in my country use two factor (a regular password and a "password card" or a password generator) authentication for online banking.
Unless some big companies (Google, banks etc) start providing this service online wallets will be untrustworthy. Security, well, some companies havve better security track record than others, so maybe they know what they are doing.