The issue of diplomatic immunity comes up all the time. The problem with erasing it here would mean erasing it from where our diplomats are, and while we have laws to protect innocents, the other places aren't so friendly. Without immunity our diplomats will be a great risk since something as simple as chewing gum in Singapore can land you in jail. I think the concensus is we gain more from this than we lose.
P.S. I think the original intent is to keep cars from being towed around the UN building. On the other hand, moving violations shouldn't be excused. Read what it says about DUI - the officers can do almost everything that would result in a conviction, but the person can disagree with everything and not be compelled to, for example, a breath/blood test. A US person would then have a second charge but the immune diplomat walks away from it all anyway, so they don't even bother.