The point is that unless you are hacked, you won't need to bother with getting a key out of cold storage. The X day waiting period could be preferable to some people than the need to get coins out of cold storage on a regular basis. For example, offline storage always requires human involvement. With the scheme I have suggested, as long as you can wait X days before spending the bitcoin, the whole process can be automated.
If you are going to automate bitcoin transactions, you need to keep a private key on an Internet-accessible computer. There is no way around that; (please correct me if I'm wrong). Once you put your private key into cold storage, you lose all ability to automate transactions.
By having 2 private keys, you can keep one online and the other in cold storage. The self-invoked penalty gives you some time to respond in the case of a compromise of your online private key.
In short, my proposal doesn't eliminate the need for cold storage. However, it does reduce the frequency with which you need to access the cold storage.
Please tell me what the "other problems" with my proposal are. I'm not so naive to think that I'll have gotten this right on my first try (or at all).