I can control the safety of my car by buying a bigger car, driving certain ways, etc. You are comparing risks you have no control over with risks that you do.
But I am in no way stopping you. Feel free to take USA public transit, and (i truly do not know how) look your family in the eyes and encourage them to do the same. I truly hope that I do not read about your or your family in the news in this light (nobody deserves that), but your chances will be higher than mine.
I don't think the statistics would bear out there being any way to make driving safer per passenger mile than public transport.
I get what you're saying. The empirical evidence just doesn't agree AFAIK.