I kind of do expect expect to leave their private matters at home. Or the very least, to handle them during break time on their own phones. This does not seem at all oppressive to me.
And in the ideal world, that's fine, but again- hopelessly naive in the real world. Taken to the extreme, why should we not record all audio? And if someone receives an urgent phone call from home, something extremely personal, should that stay in the company's records? No, for fear that the company will use their power disparity to exert undue control over the employee's life from them attending to the actually important matters in their life. That's why privacy matters.