CarPlay enables a car-friendly interface with big buttons, shortcuts to navigation/music/communication, and minimal distractions. I don’t know of any way to get that on the phone’s own display.
That's not Android Auto, it's Waze doing that (and it would do it on Apple too). And it's not "an attempt at engagement", it's a cost for keeping the real-time map and traffic data that Waze is chosen for up-to-date. Use Google Maps if you don't like the interruptions.