As soon as you add management into the mix, people get cagey and the standup becomes less effective.
I'm a PM now and I run my team's standups, but even that may not be ideal depending on the perception of PMs within the organization. I think it's great when there's a tech lead or senior team member who wants to do the job -- they have the authority and experience to resolve issues quickly, but are still perceived as a collaborator, not a supervisor.
You're management, you are not communicating laterally.
But I openly acknowledge that PM can be perceived as a tentacle of management, which is why I said it's not necessarily right to follow my current example.
I have never seen this in 20+ years of work.
Management is supposed to be in the standup to help remove blockers.
Scrum Masters should also be just a member of the team, not a "master" per se.
The addition of management always turns it into a status update.
I wasn’t yet taught why managers do nothing when you have long-standing discontent :)