It's desirable to allow other zkapps to read your state without needing a proof (which on L1 might not even be feasible because of account update limits), but setting access = None also means your zkapp can't be a token owner practically, since all token logic would be completely unchecked.
A simple way of doing this would be to check access permission only if account update has children.
It's not clear to me what the original motivation for the access permission was beyond token owner control.