Good idea, for anyone that doesn't want to have to get up inside the door and deal with a bolt head, or nut, and washer.
But, the contact and 'gription' that you are getting by doing that, is not all that much more than just screwing through the panel with a self tapping screw.
The best connection for something that is going to hang off your door panel and vibrate the way the mirrors do, is to drill through, use a bolt and nylock nut, and two fender washers. One washer inside, one washer outside.
A good solid connection that is much less likely to rattle loose, and protects/strengthens the panel, rather than stresses it. No special tools or techniques needed.