The name "one-on-one" seems to answer this question, but I'll ask anyway. Would it be appropriate to sit in once in a while on my directs' O3s that they hold with their directs?
I have four directs. Two of them collectively have 5 directs. I do not mandate that my team listen to Manager Tools or follow the guidance. Nonetheless, both of my directs who are managers conduct weekly O3s. My directs hold their O3s via Zoom, so I could just sit quietly and observe - even muted with my camera off. In terms of frequency, I'm thinking once or twice a year.
I have no concerns that my managers are doing anything wrong. Their teams are productive and seem happy.
I thought it might be worthwhile to sit in on their meetings once in a while to see how they conduct them and, if appropraite, offer feedback. It might also give me deeper insight into the priorities and challenges of both my directs and their team members.
I do have a concern that doing this might undermine my directs. I asked myself how I would feel if my boss asked to sit in on my O3s. My response to that would be concern that he is unhappy with my performance or the performance of my team. I suppose this could be managed by, at the outset, explaining that I'm asking to sit in to better understand how my team conducts meetings, and that I have no concerns with anyone's performance. I'd need to explain that to both my directs and their directs.
Is this a good idea? Or should I file this away under, "If it ain't broke..."?
If you're happy with the team
If you're happy with the team's performance why would you want to take this step? You should be meeting with skip levels but not often and not one on one. Mark often says "don't do anything you wouldn't want your boss to do".
From "Don't Do Skip Level O3s"
3. Have Skip Level Meetings
All this said, we'll still want to trust but verify when it comes to your skips. We do that not with Skip O3s, but with Skip Level Meetings. You can be completely forgiven if you have heard "Skip Levels" and assumed that somehow they were one-on-one meetings. Some managers do use it this way. They're not wrong, they're just doing the best they can with poor guidance.
Skip Level Meetings - and yes, There is A Cast For That - are GROUP meetings between you and several or more of your skips (depending upon spans of control). Our cast on it lays out how to structure your agenda.
Noteworthy: your directs are NOT invited to a Skip Level Meeting.
Skip Level podcast: https://manager-tools.com/2006/04/skip-levels?start=1420
Don't Do Skip Level O3s podcast: https://manager-tools.com/2020/05/dont-do-skip-level-one-ones?start=1564