There's also another possibility, albeit less likely, that the FBI know they'll lose but they don't care because they can already read the device and they want any terrorists to believe they don't have the information on it. That's a pretty full-on "tinfoil hat theory" though.
Besides, if this particular information is that valuable, they would have no problem paying for it.
Which brings us back to: it isn't the device they want cracked, but governmental oversight of (civilian) encryption.
So they can't just attempt to brute force the encrypted data, as the encryption key would be 256 bits or more rather than just a 4 or 6-digit numeric passcode. That's why they want Apple to open the OS up to brute force passcode attempts.
Edit: there's no secure enclave chip on the phone in question, but it seems that iOS 8 and later encrypt the user data with a separate private key combined with the user passcode.
The password is tangled with the UID burned into the device at its creation, creating the 'passcode key' that secures the phone[0].
If extracting the UID is somehow possible, it doesn't sound impossible to try all 10,000 combinations (assuming the a 4-digit passcode is used) offline, on different software.
[0] - http://blog.cryptographyengineering.com/2014/10/why-cant-app...