Whether or not they invade your privacy, they reduce your idea of your health to a set of numbers that are divorced from the actual reality of your life and your overall wellbeing. Just abstain!
Not everyone does it, but most of the folks that don't will do so if they are doing things like trying to get pregnant, know when their mood will change, or are having other issues. I'm pretty sure that menstruation issues are the real thing that lowers your overall wellbeing. I've experienced this very thing, and I've needed the dates when things have gone wrong... or simply when I have had to go to the hospital/doctors, since they always seem to ask when I first started my last period.
Something on your phone simply makes it easier, especially since most folks take their phones into the bathroom with them from time to time. I just use a notetaking app, though, mostly due to privacy.
We know that there are benefits to tracking your blood pressure at home, for example[0].
In addition, and closer to the topic in the original link, there are simply concrete benefits (ie: birth control) to an app like Natural Cycles[1], which involves tracking your temperature and period in an app. I understand that for some people this type of additional option may be difficult to appreciate, especially if you're not a potential user. It requires a lot of discipline: taking your temp consistently and at just the right time. But for women who might not be interested in or respond well to hormonal birth control, it can be an invaluable tool.
Even for normal period tracking apps: tracking one's period _can_ be useful. It can help to monitor fluctuations that would otherwise easily go unnoticed for longer than they need to. I've had friends who missed very early or late periods for months before they realized their schedule was off and that it might be something they should see a doctor about.
In conclusion, this "all apps/tracking health data is useless" sentiment that gets thrown around so commonly does not really seem to be in touch with reality.
[0] https://www.health.harvard.edu/heart-health/how-to-monitor-a...
[1] https://www.fda.gov/news-events/press-announcements/fda-allo...