Earlier quoted context omitted.
Technically, Ubiquiti does have a local option. You can run the controller locally and disable cloud login.
Protect still needs cloud to be activated for authentication it seems. I used to have remote access turned off and accessed the video streams via the iOS app when my phone was on VPN to the local network. That no longer works. Remote access (cloud) needs to be activated in order for the iOS app to work, no matter if you are on the local network or not.
My controller is only on 6.0.43 but i can access it via iOS app on VPN.
My contoller only does Wireless/AP management though. nothing more.