Ohh - I see.
To allow someone to see your profile information a user can enable "Preferences > Privacy > Show Private > Information in Profile to...
I tested this and it does show the AboutMe section publicly.
I didn't notice anything else it exposed but it didn't show email or ip address or anything so it *might* be what you are looking for.
That said...Title, WebPage, etc were (I suspect) removed from the header section at launch for two reasons
1) they were ugly and cluttery OOTB and
2) they looked like they would expose information we didn't want to drop without full inspection.
We err on the side of caution when it comes to PII (we were burned pretty badly before).
That said, I understand your request ; we are community of humans and it would be nice to get some *humanity* back in the mix.
I can't promise much right now but I'll see if I can figure out how to add at least Title, WebPage, and at least the available components on the Profile Settings - back onto the View Profile Page.