User friendly wallet with client side keys and autobackup

I read a post today about a company launching a wallet and they said that they needed to store the user keys on their servers because having private keys on user devices requires a user to backup their keys which is not user friendly.

It's a bit new this idea. Not sure if it's already out there. I believe there is a better way to have client keys and the user friendliness of no backups using timed locked transactions. Use timed locked transactions to send the coins to a recovery address if the user does not sign in after some time they become valid. Each time the user signs in the user nullifies the old transactions and pushes the expiry day forward. The wallet would need to re-sign the timed locked transactions every new transaction from the wallet. That's the basic idea without the details

The risk is only if you fail to sign in after x days and let's say CompanyX had to hold your coins until you request them back. Otherwise your private key would always be local and not shared with anyone.

And you could make the recovery address another one of your own addresses but the point is to be user friendly. And the recovery address is a last resort.