To start, there are two things which any discussion on this subject has to start from:
1) Sending and receiving '+owner' messages are two sides of the same coin.
2) Within groups.io, 'Moderator' can mean many things from 'owner in all but name' (with full powers) to 'trusted member allowed to do a few extra things' (that ordinary members aren't)
Having said that, my thoughts are:
1) The ability to send and receive/read '+owner' messages should be a moderator permission, granted by the owner as others, and with three options: (i) send and receive/read; (ii) receive/read only; and (iii) no access. (whether it can be done as one, or needs to be done as two, is a technical issue).
2) Whether a moderator (permitted to receive/read such messages), receives them as e-mails, or is just able to read them on line should be a preference they can set, as with ordinary group messages: whether it can use the same preference setting(s) as ordinary messages, or should be its own setting, is something I'm ambivalent over.
3) There follows a group management issue (nothing to do with the technicalities/software/group.io service per se), that the owner should be clarifying his expectations to any moderator with this privilege - as to whether they should be pro-active and instantly responding, or not.
So I think I'm essentially with J_Catlady on this one.