you just explained it, they're not coin operated.
Though occasionally you saw a cart far far away from a supermarket, where someone had basically stolen it, either teenagers to have fun, or someone asocial who, I don't know, used to carry all the shopping home? I don't really know what they did with it.
And it was the cost of replacing those stolen carts that drove the adaption of the coin operation system. Not that people just left them in the parking lot. Some supermarkets also tried a system where the cart locked if you moved it out of range of some radio in the supermarket, but that one really didn't take off.
(Also, quite a few people in Germany just do shopping by walking or biking to the supermarket).
And now they are again. Some new REWE carts already come without this feature.
Museums, libraries, and train stations aren’t places I go weekly, like a grocery store. When I do go, I can’t remember the last time I ever used a public locker. I can count on one hand the number of times I’ve used one of those in my life. I don’t tend to carry much stuff with me, so a locker isn’t something I generally need.
I was once 75 cents ahead by the time I made it inside of an Aldi in Columbus, Ohio because there were 3 free-range carts in the parking lot that I returned. Three was a lot -- most days I only found one cart hanging out in the parking lot.
In my current neck of the woods things are a bit different. There's never any carts roaming the parking lot, and there's usually carts with quarters already in them, parked properly up by the door.
(I often leave one parked with a quarter like that myself, but it's not because of some "pay it forward" quasi-altruistic purpose or something. Sometimes I just want to pick my groceries up out of the cart and walk to the car and I just don't have enough free hands to deal with retrieving the quarter. So I line up the cart with the others, grab my bag or two of things, and shove the cart the rest of the way home with my hip.)