The average ‘website user’ does not right-click to find the info, so I see little point in that argument. If there’s an OSM-based service offering to source address info like that, then they (as data users) need to figure out how to optimally present data to their end users.
As for your other question:
You may have noticed there’s no official source of any kind around, open or closed. I’d guess it’ll be a near-match, but I doubt it’d be a perfect one.