Pre-covid, I only ever had manager 1:1s in a meeting room, or much more commonly, walking around the campus. Very occasionally a 1:1 in a deserted corner of a cafeteria during non-meal hours.

A manager 1:1 in a nonprivate space sounds awful.

I would argue a meeting in a non-private space isn't a 1:1 at all. That's awful.

You're right - any conversation at people's desks in an open plan office should essentially be considered open for anyone to listen and join in. Otherwise it's just plain rude or inappropriate.