The points are for removing the electrostatic charge that builds up on planes. An air plane moving through the air builds up a static charge, just as rubbing a balloon on your hair does. (Yes, I have enough hair left to do that.) On a smooth surface, the charge will spread evenly, but if there is a point sticking out, quite a bit of the charge is concentrated at the end of the point, and transferred to the surrounding air.

That is why the tops of Van de Graaff static machines (the devices that make your hair stand on end) are spheres. With no corners or points, the charge stays in place. If the metal sphere gets a scratch or a dent, the charge drains away, just as it does on the air plane wing.