It's less about keeping people engaged and more about making everyone in the team understand how it should be ran. Once you run these meetings a handful of times you start to appreciate that people coming in late or giving nonsensical contributions is irritating and the outcome is that the individual who ran it ends up contributing better to the same meeting next time.
This goes for all meetings (and literally all roles in all workplaces even outside of tech). It's there to build first hand understandings and empathy and, if these meetings are a waste of time, empowers the entire team to change it or abandon it.
I dunno when I run standup I am just as passive as when I'm part of it. I just prompt people to speak and then zone out if its not useful like every time.
I feel like having to resort to tricks to keep people engaged in a meeting is a good sign that the meeting isn't a good use of time.