permissoned zkRollup with private smart contract?

Hey guys!

Recently, I deal with ETH scalability solutions and I started to read more about zkRollup. All found solutions are permissionless and do not deal with privacy (except Zcash which allows anonymous transactions).

In my opinion, zkRollup can be easily used as a permissioned/consortium system. The basic implementation to make this kind of system is not a big deal. My main problem is privacy and group handling.

Except for the global public state (public contracts), each group has to deal with its own contracts and do its own zk proof generation. Thus, it seems to be an enormous waste. I do not think it is a good approach to the problem. Sidechains and plasma can be a better choice.

Requirements: the new system has to be capable of transferring (mainnet's) Ethereum assets, executing public/private smart contracts, and storing some states or proof on the mainnet.

What is your opinion about this idea?

Is private smart contract a possible thing in a permissionless or permissioned context?

Thanks a lot!

edit: it is not necessary to be a permissioned system