Is it feasible to remove non-functional via pads on outer layers
No, you can't eliminate the outer-layer pads on vias. As described here, the final etching step occurs after the plating step. The outer pads serve the very important function of protecting the plating inside the via from the final etch.

Specifically, the plating step is normally done through a mask, so that only the traces and pads on the outer surfaces are built up with plating &mdash; first copper, then a thin layer of tin. Then the photomask is removed, and the tin itself serves as the mask for the final etching step that removes the unwanted original (unplated) copper on the outer layers.

A via can be plated only if the electrolyte can flow through it. If you omit the surface pad, then the hole will be partially or completely covered by photomask on that side, limiting or stopping the flow of electrolyte. Furthermore, even if plating is successful, once the photomask is stripped for the etching step, the exposed edges of the plated copper inside the hole will be undercut by the etching process, seriously affecting the reliability of the via.