You cannot sign without putting all your key parts in one place. If that one place is compromised they will be stolen or subverted to sign a different transaction. If that place is completely secure you can just put a single key there and dispense with the fancy footwork.
Yes but don't multi-sig or secret sharing suffer from the same problem? I still need to collect all the parts in one place when I want to spend my coins.
The generating of the private key and the recombining will all be done on an offline computer. I could just keep one key on the offline computer, but if its stolen I'm screwed, whereas 2-out-of-3 gives me backup.