> If you maintain the price at "free", demand saturates and people stop stealing carts.
If the price is $1, the same people who'll steal them will keep stealing them (with a screwdriver it's easy to pry your coin back out of the slot anyway).
> it's also not rare for people to just leave the carts somewhere convenient for them
With the coin, guess what... it will be rarer, because the people have incentive to get their coin back. At least in theory. And if someone doesn't care about their change, some enterprising kids might return the carts anyway to gain some money, and the end result for the supermarket is the same: carts at their designated return locations. The worker just has to go to 3 or 4 of these locations instead of running up and down the parking lot collecting all the stray carts.
It’s compounded because they’re also the only store near me that doesn’t have handbaskets, so you need to either grab a cart or hope there’s a loose cardboard box in the store (which there often is because they expect customers to use them, but you may not find it quickly).
There's no particular need to change this, because one person can only use so many shopping carts. If you maintain the price at "free", demand saturates and people stop stealing carts.
It's common for people to return carts to a designated area, and it's also not rare for people to just leave the carts somewhere convenient for them. Store employees periodically go around and move the carts back to the place where you expect to pick them up.
Costco is an interesting hybrid case. They make it easy to return the carts "correctly" by providing little depots scattered throughout their enormous parking lot. Realistically, the parking lot is so large that very few people would be willing to return a cart to the front of the store, where you get the cart from if you're going shopping.
However, people also aren't going to pick up carts from those depots deep within the parking lot and wheel them over to the store. So Costco employees still have to make rounds of the parking lot and move carts that have been left there to their correct location at the front of the store. But for Costco, you're supposed to leave the cart in the parking lot, but only in certain locations.