I think asking for cams to be switched on is totally reasonable. The only acceptable reason against it is of technical nature like bandwidth or that your laptop can't handle the load.

Having said that - I also avoid switching on the cam. But from the perspective of a manager intending to lead a team and a team member interested in engaging with colleagues it does make total sense. Why do I still don't have the cam on usually - because I neither like my work place nor my team at the moment. And I suspect that's also the case for you.