Since we can store the wallet balance in the chain
We don't and we can't, so the rest of your suggestion is invalid.
True.
Likewise, if I understand what you are suggesting, I do not believe this adds anything in terms of security that could not be done at the application level vs the protocol level. In either case (creating/changing your rules with your private key etc) vs bitcoin as it is now, if someone has your private key, you are screwed because they'll just change your rules and then transfer your coins. A root cause of insecurity is protecting your private keys and adding these rules doesn't help with that.
I must be missing something - explain to me how bitcoin stops people spending more than the balance of their address.
The rule key is required to remove a rule.
The rule key is more secure than a private key, because you dont need to use it all the time, and it only ever gets used once - to remove a rule.