Our club currently has the ability to add/remove members 'off' because we're not able to be notified or approve when someone makes this sort of edit. Here are some example rules we would want enforced.
1. No one with the member type of "bond holder" can be removed from the account. (This often happens when couples are getting divorced and the billing contact with access attempts to remove the spouse)
2. Only 1 caregiver per account.
3. Only 2 Adults or Bond-Holders per account (unless they contact us and there's a special circumstance with multiple adults in the household)
I would love a way to just be notified when any add/removal of member or changes to someone's name. This would solve most of these problems. If someone adds more than the allowed number of adults or caregivers, we'd catch it during the notification and email them about it.
We also have this feature turned off for similar reasons. Instead, we created our own custom form for adding members and have a message on the account screen to ignore the Add Member button. This solution is not working perfectly because people would rather click a button than read a message!
I created a filter on the Members screen that adds the Date Registered (or whatever it is called) column, then sort descending by that. I check it each day to see who was added, and then contact the members as necessary. But setting limits by Member Type would be nice (I suggested that, too). And I like your suggested for admin notifications of changes. I'd like to expand that to photos, too.