I would pay a lot to have this on iPhone as I'm distracted easily due to my ADHD. iOS doesn't have as granular notification configuration as Android (topics?) plus Apple probably wouldn't agree to funnel all notification through 3rd party app.
You're right - the app sandbox model in iOS prevents inter-app communication of notifications, and there is no iOS equivalent to the Android ListenerNotificationService API.
For me the biggest pain was email.
I created a free and open source set of filters to fix this. Soooo much better.
This is what drove me to uninstall Facebook, twitter, etc. I use their websites if I occasionally want to visit. I don't want notifications hooking me into my phone.