Terminology note: the base of a plane is referred to as the sole.
Grooved or corrugated soles were intended to reduce friction by reducing the surface area of the metal plane in contact with the workpiece. That's the theory at least. The fact that corrugated soles did not continue to be made probably indicates most strongly that they didn't offer any significant advantage.
In the modern era, more than one woodworking guru has commented that they cannot notice any difference in use, especially if the flat-soled plane is kept properly lubricated with wax or tallow. Chris Schwartz for example notes: "I have planes with both smooth soles and corrugated ones, and if there is a difference in effort required to wield them, I cannot discern it."
(Read full piece here for further details as there are other advantages.)
especially since planes are often used at a skew (turned slightly from the direction they're being pushed).
Keen observation. I have wondered the same thing myself, and have been told that it doesn't make any difference. On wood that is already fairly smooth I can buy this but on wood that is still quite textured I can't imagine it wouldn't make at least some difference as there are multiple arisses moving across the texture versus just the one on the leading edge of a regular plane.