Common coin in private network

[skhoroshavin]

This is actually a question about protocol, not an issue.

I think I do understand why threshold signatures are needed for common coin in case of open message exchange in public network, where some malicious party can intercept, read and delay them in some smart way. But is cooperative calculation of common coin value is really needed in a network where all nodes are connected only by p2p encrypted channels? Can some kind of hash-based pseudorandom sequence (or just round robin) be used if there is no way for a third party to decrypt messages between any two given nodes unless one of them voluntarily disclose them?

I'm asking because lifting requirement for threshold crypto could simplify honeybadger a lot and make it even more attractive as a PBFT replacement in private or permissioned networks.