I can’t find anything for a private tag in the wiki. Which implies it’s not valid usage.
I believe iD interrogates the database to find keys and values that have been used by others in order to guess what you might be trying to do. In that respect the database (and hence iD) is like English dictionaries and not French ones. English dictionaries reflect how people use (and misuse) language; French dictionaries tell you what is permissible. So anything that has been used/misused/abused in the past will be available as a suggestion in iD. Even typos.
I’d check with iD but it’s not been loading properly for me for the past three days. Despite begging people in this and the editors fora to tell me if iD is working for them (so I can figure out if it’s me, my ISP, or iD’s servers) nobody has responded. If you could do me a simple favour…
Not many. Not many at all.
Or you could use access=residents. Around 950 people have used access=residents; around 80 people have used private=residents.
private=employee or employees has not been used. private=staff has been used 6 times. access=employees has been used 315 times. access=staff has been used 138 times.
https://taginfo.openstreetmap.org/