This is not about private or public data. The definition of personal data is strictly defined in GDPR. It's about data that can identify you as a specific natural person. These can be direct data (name, surname, ID, address details, etc.) or indirect data (eg a description of the person, description of its features, behaviors, etc.).
You should read GDPR and then we can talk.
So if someone gives a phone number, it will be a personal data, regardless of whether it is written in public or PM. If someone will describe that the flowers are colorful, it will not be a personal data even if you write privately in PM (private data) or public in post.
Froddelaar that's right! Not many people understand it.
What we can do to prevent loose posts it's another topic.
Please do not mess with David's topic. I wrote about the GDPR in another thread and invite you there.
If David adds the feature to download and the ability to delete a user account or complete anonymization, it will be fine. But maybe it's too much for one man. There is another extension for deleting users from UCP by themself.
I agree that it destroy the flow of topics, but notice that FB or Instagram user can deletes whole thread which he started including comments of other users.