Sure, but the change in the client won't change anything. Anyone can watch your notifications if your inbox relays allow them to. Especially if you use public/free relays.
Yeah, but this makes it really easy. Just install the app and plug in the npub of the person you want to monitor. Even if it doesn't solve the greater issue, requiring authentication would close a pretty big door.
It's already easy. You can use any client to watch others. Just log into primal, amethyst, damus, etc.