Sure, but people close the door out of modesty not really privacy. If there was a machine that provided a written transcript of what someone did in the bathroom with no video/audio I don’t think people would mind.
Like when you’re in high-security areas and have to be monitored in the bathroom there might be a door between you and your guard but no real privacy.
Or when people loudly object to strip-searches at the airport but the scanner that sees everything but then only shows a cutout highlighting suspicious areas to pat down are mostly fine.
I think it's a pretty good workable analogy actually. People don't mind if you know they go to the toilet as an abstract thing, but once you start keeping a notebook of who is going to the toilet and when it starts getting creepy and undesirable. And that's just for collecting metadata! imagine if someone would actually intercept your sewer and analysed the makeup of your turds, folks would be up in arms.
We need this information to correctly gauge the interest on different kinds of foods we should keep available to purchase in the cafeteria.
It's also helpful as we can notify you early if you have some undiagnosed medical issue. You could unknowingly spread your illness to your children without this early detection.
We're even able to reduce your monthly health insurance premium by providing this data to the insurance company!
This also enables us to find troubled Individuals before it's too late and address building drug issues before they're full addictions. We'll be able to get them the required attention they need to get back on their feet and be productive members of our society. (Maybe not here though)
Like when you’re in high-security areas and have to be monitored in the bathroom there might be a door between you and your guard but no real privacy.
Or when people loudly object to strip-searches at the airport but the scanner that sees everything but then only shows a cutout highlighting suspicious areas to pat down are mostly fine.