A car does build up a charge as it drives, but the charge dissipates very quickly to the ground through the conductive rubber in the tires once it's stopped. When you get out, if you haven't dissipated your charge slowly by touching metal first, the charge will suddenly arc as it discharges through your hand, into the door and then to ground. The grounding straps won't change that, as the idea behind them is to assist in dissipating the car's charge.
If I don't touch anything as I get out of the car I'll sometimes get zapped and see the blue spark when I touch my metal garage door handle.