Of course, that only allows for exporting data out of your app. If you want to import data or work with it this doesn’t really help.

You could always create a Shortcut and add it to the share sheet....

Honestly, I think this touches too close to the “default apps” issue that Apple has been quite recalcitrant on, and in my opinion it won’t be fixed until they change their mind on this. They have the technology in place to do this safely, so at this point this has to be a choice they’ve made. However, to address a specific concern about your first point: I do find it convenient to have one central location for all these things, as opposed to a dozen different home automation and health tracking apps or random folders on my filesystem for photos. Apple might be heavy handed in limiting categories here because it keeps data consistent and prevents issues where years of menstrual cycle data was being added under a custom “Periods” category and format that’s incompatible with this year’s “Cycles” measurement.