Nothing, but no one will/should trust them without cryptographic expert consensus saying it's ready. Right now, the cryptographers most familiar with it are working on/with the official team and aren't clamoring to release it yet.

And anyone doing an early release will need to handle the initial parameter selection which has to be done publicly/securely to convince people that the private key toxic waste (that would theoretically allow counterfeiting) wasn't retained.

They are planning a secure multiparty computation that never creates the private key in usable form provided that at least one of the n parties follows the procedure correctly. This again relies on expert consensus that the process is secure.

On a side note, this is likely to produce some fun spectacle: I fully expect someone involved will try to verify they destroyed their private key share by live streaming the generation process then immediately and totally destroying the equipment involved.