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Period tracking app refuses to disclose data to American authorities
(www.newsweek.com)
This is a most excellent place for technology news and articles.
Ok yeah, I understood everything in your first paragraph. The privacy part was what I was really asking about. So if you're not self hosting you're still at the whim of the person/company/whatever that is.
You could also argue that if even if you're not self-hosting (i.e. renting server hardware from a 3rd party), your data is still in a siloed environment. While it may be accessible by law enforcement if you are targeted specifically, it's unlikely to be dragnetted like the data collected from popular apps.