But by what morality is that a problem? Driving itself puts lives in danger. Why is the risk to them worth more than my timeliness?
What reasoning?
Are you really asking why we value an individuals life/well-being over your desire to speed? It's based on the premise that you have a right to your life and those who would take that right away through negligence or malfeasance are doing you harm and not acting morally. As far as the risk of driving even within the speed limit laws, it's just a risk we accept for convenience. We try to mitigate the risk as best we can though driving rules and regulations.