Normally a director provides an address to which email can be sent and no one questions it.  I assume that your concern is about confidentiality, although I am not sure how much would be so confidential that a spouse couldn’t see it.   But if people care about confidentiality and don’t want material sent where the spouse can see it, the board could adopt a policy of not sending email to the joint account and sending all info to those members by regular mail, or sending confidential info by regular mail while emailing those things that are not confidential.  The second alternative requires decision-making with every email, which could be a real pain.

The organization has to be able to give notices and send information, and I don’t think there is any way it could force a person to get a personal email account, although the board might raise the issue and request it.  (If the board really cares and has the right bylaw provisions, it could remove a director who refused to get a separate account.)  The director might decide to get a separate account if info is delayed because it comes by regular mail.

I suspect that the reason you have not been able to find much on the question on the Internet is because (1) there are not a whole lot of people who have only a joint email account and (2) for those who do, boards don’t particularly care.