It's a ventilation and safety thing.

First, it seems that public restrooms aren't built for utter privacy and secrecy, but merely dignity, and blocking out the main parts suffices for that.

They're public spaces, so it's sort of helpful that I can detect someone using a stall, rather than walking in on them. At least I feel OK if someone couldn't lock that broken door (happens so often!) that I'm not barging in unbidden. There are often parents with young children who may put them in a stall and wait outside. (Not at a place of employment, but...) It's good that they still have some contact through that door.

Also, ventilation, right? A completely enclosed space with a tight door is going to get smelly, and that's not easy to clean or maintain. A partly-open stall is going to exchange air with the rest of the room, for better or for worse!