In reply to Otto.
More like we need two separate email addresses recorded in each site’s settings: 1, an general/admin email address, and 2, an alerts email address.

The admin email is used by plugins for mixed purposes such as a) to send alerts to the site admin, and b) as the default address for contact forms. Many developers set the site admin address to their own email address instead of the site admin’s/owner’s email address because site owners/admins have a natural hate of what they regard as spam, inclusive of the ‘Your site has been updated to…’ emails sent by WordPress. We need an option to set an alerts email address and a general purpose/admin email address.