Feature phones are still a thing, and they are even more private when you allow the battery to discharge completely. Track me now, guys!
I am not defeating the purpose, though. A charger in the car brings the phone to full function in a few seconds, in the event of car trouble or other unusual circumstance. It doesn't need to charge a bit first. If there's a preplanned circumstance when a mobile phone will be useful, like meeting someone away from home, I can easily charge the phone; it reaches full charge really quickly compared to smartphones, and it can be on standby a week or more before it nags me for low battery (and it's about 7 years old, with the original battery).
Otherwise, I use old-fashioned land lines to talk to friends or family. If I am out and about, I finish whatever I am doing. I'm then free to return home and call anyone I want.
I didn't need to be constantly connected in the 80s and 90s (I didn't get my first mobile until well into the 2000s), and I'm still the same individual I was then. Why, back in my day, I... well, never mind.