I’ve used Debian for years on my personal machines and have never had this problem. According to Debian’s documentation for NetworkManager, a user account must be in the netdev group in order to manage system-wide network connections. The initial user account that the Debian installer creates for you is in this group by default, but maybe the accounts you created for your family members aren’t?
It’s not just “hardly anyone,” it’s “literally no one.” Varlink was invented by the systemd developers out of whole cloth specifically for this purpose.