What is required to spend bitcoin is that input be provided to the UTXO script that causes it to return true. What Chris is proposing breaks the programmatic nature of the requirement, replacing it with a requirement that the secret be known. Granted, the secret is the only requirement in most cases, but there is no built-in assumption that the script always requires only that secret.
This idea could be applied by having the wildcard signature apply to all UTXOs that are of a standard form and paid to a particular address, and be a signature of some kind of message to that effect. I imagine the cost of re-scanning the UTXO set to find them all would justify a special extra mining fee for any transaction that used this opcode.
Please be blunt about any of my own misunderstandings that this email makes clear.