There’s definitely solutions to the problem. You could carry disposable gloves. People with dogs carry plastic bags everywhere. That could work in a pinch. You could wedge the door open and use your foot to open it to leave.
I personally just try to not use public toilets as much as possible. I carry hand sanitizer spray and a bottle of water in my backpack. It’s definitely gross, but it’s not unsolvable.
Use the paper
There’s definitely solutions to the problem. You could carry disposable gloves. People with dogs carry plastic bags everywhere. That could work in a pinch. You could wedge the door open and use your foot to open it to leave.
I personally just try to not use public toilets as much as possible. I carry hand sanitizer spray and a bottle of water in my backpack. It’s definitely gross, but it’s not unsolvable.