I'd really like my phone to be able to prioritize notifications and only bug me for important things. Calls, SMS, notifications etc should all be hidden and prioritized. A call from my wife, or someone I know should be immediately shown. Notifications about important emails as well, not so much about the latest offer available on amazon.com. Phones make it hard to control the level of notifications and could do a better job at that.
In android there is a "do not disturb" option that silences everything but calls (you can drill it down further to starred contacts or none at all) and sms messages (also drillable), I always have this on.
I turn off read receipts where I can, allowing me greater control of when I respond and I also silence group chats and people who are bothersome indefinitely. If they are important enough I will find time to answer them, regardless of how "noisy" or "noiseless" they are. If it's urgent, they can call.
You can install a pihole server at your home that will block advertisers through DNS, allowing you to use even free apps without ads. (I haven't done this yet since I moved recently).
As for emails, I imagine you can have a single email address on your phone for important emails and configure email forwarding rules from your default email, I haven't tried this though.
Gmail with the split inbox has that feature (although for the life of me I can't get it to put updates/promotions into the same bucket, though they are) and inbox allows you to bundle and split things even more.
