I use Any.do (which I like the UX off a great deal) with Reminders for this, at first it felt like it was nagging the hell out of me since I was snoozing so much stuff but then a strange thing happened, I stopped snoozing stuff and started doing it so I could kill the task if it was a quick task.
On the UX side something like that has to be so effortless for me to use (ymmv on what effortless is) that it becomes a habit otherwise I just forget to enter stuff as it occurs to me.
What I'd really like is an unobtrusive bluetooth like headset with natural language processing (think miniaturized persistent Alexa) that didn't need to sync through my phone but could sync with it periodically.
"Hal, task: remind me to buy cat litter, tomorrow morning, 10am, remind me again at 1pm"
"Hal, remind me, Monday morning, 10am, task: check I answered email from FooClient"
Then at 10am Monday morning audibly "You have a task: check you answered email from FooClient" "I've done that"
"Hal: Snooze all notifications for 2 hours" (for when you don't want to be disturbed) and have it cue up anything in that period.
"Hal: while I was snoozing, you missed the following tasks" etc.
Most of the pain of using a phone for task management is that typing stuff in is still annoying, on the technology side we are pretty much in that direction already I've even considered buying an Echo and seeing how far I can get with it's API.