A possible solution would be to run all third party apps in containers and use computer vision (deep learning) to collect messages and notifications from their screens into a single place, if they don't want to cooperate officially. I don't know the legal implications though.

Another app that should run into a container and be post-processed by computer vision is the web browser. We need to contain the browser itself (more privacy) and keep the pesky ads out of our eyes in a way that is impossible to hack by clever scripting or ad-block detection. On the next round, ad publishers would have to create adversarial ads that fool the classifier which would be a whole lot more difficult.