I have always had trouble with a similar argument to part of the one you set out above, and I have trouble finding a good response to it. Maybe someone can enlighten me.
The argument I have had presented to me is that the monarchy, no matter how good a job it might do, perpetuates the idea that some people are born "above" or "better than" others, or even "different than" others. That they deserve their position by an accident of birth alone.
Can someone help me!