What is the point of having a mnemonic recovery seed if it's useless for anything other than recovering on THEIR website?
The point of it is to recover your identifier and/or password if you forget them.
Can I use this recovery seed anywhere else to recover these coins?
No. It isn't a "recovery
seed" it is only a mnemonic for your identifier and password. The identifier and password aren't useful anywhere else.
What am I missing here?
You are missing a backup of your wallet. You really should have stored a backup copy of your wallet in case blockchain.info were to ever become inaccessible
Anyone have any ideas?
Contact blockchain.info support. Wait for them to find the time to respond to you. Good luck.