The bathrooms are just indicator that the problem exist and that it should be solved. So - the gradual approach is the best: a bit installation and a bit cultural intervention and then - more installation and more intervention.
No, the answer is separate bathrooms for boys and girls, with stalls that have fail-safe lockable doors (just like at home), and then perhaps a third private (1 stall/toilet) bathroom) for those who
experience “bathroom anxiety” when being in the bathroom with pretty much anyone . ALL of these bathrooms must be cleaned and maintained so that no one gets made fun of for having to use the stall with the toilet that always overflows, or the toilet that always smells “stinky.”
Good heavens, many new homes in the U.S. have a separate “master bathroom”, a separate “children’s or teens’ bathroom”, and a separate “guest bathroom,” and if there is a basement, a separate “workshop bathroom” for whoever is working in the basement. If we are so self-conscious and needful of privacy in our own homes with the people we love, then it makes sense that we are also self-conscious about being in a school or office bathroom with multiple stalls, often with unreliable door latches that spring open at the worst possible time!
Yes, I realize that there are homes where abuse is happening and all of life is stressful–I’m just talking about “normal” homes here, OK.
Yes, I realize that in the armed services, you might not even HAVE bathrooms with toilets and have to use a tree and dig a hole. Well, that’s military life for you–but school is NOT military life and the children/teens are not soldiers, sailors, etc.
Yes, I realize that in the poor countries, there are no indoor bathrooms, but just holes in the floor and kids use them without being afraid–but we’re not IN a poor country.
Yes, I realize that kids should grow stronger spines and not be upset or non-plussed or (horrors!) start crying when fellow kids make fun of them, especially over bathroom use. Too bad, so sad–it’s not going to happen. When you are made fun of, your spine turns into a big soft licorice stick, your brain dries up and forgets all the de-escalating phrases that you were taught in “Stop Bullying Now!” classes, and not only do you cry, but you sometimes go potty in your pants out of fear.
Let’s just build public bathrooms that are appropriate for this day and age where bullies have rights, too, and someone who fights back will probably end up in worse trouble than the bully.