Would this wallet backup system work? I was thinking about a possibility to overcome the 'only stored on one PC' wallet problem! I erase or lose my PC, then I lose all my bitcoins.

Suppose that the wallet, associated with an account number and a strong secret password were backed up on all Bitcoin clients.

What would be the drawbacks/advantages of this solution?
In a way, this is how deterministic wallets work: All keys and addresses are derived from a secret pass phrase. The "wallet" in this case is the description of the algorithm, which is "stored" publicly.