Via pads on top and bottom layer are required for regular through-plated drills, otherwise the vias must be produced as blind vias. Unconnected pads on inner layers will be usually removed anyway.
The usual (less expensive) way to achieve what you want (remove stubs) is backdrilling of vias.
As FvM already stated, the easiest way to do is using blind via's from layer 1 to layer 2. An other option is using a double core construction.
Instead of using one core and two copper foils you can also build a 4 layer board with a double core construction.