The Van Geet is specifically 1.Nc3 d5 2.e4 d4, not the whole Nc3 complex.
It is not played much because of d5. With 1.e4, you are covering d5. You either eliminate it with exd5 in the case of the Scandinavian, prevent it, like in the Sicilian, or block it with d4 yourself like in the French or Caro.
1.Nc3 does none of this, and that is not good for the same reason that you do not play Nc6 or Nc3 in Queen Pawn openings. You typically want your c-pawn advanced first, or sometimes it uses that square for Defense (especially Black).
The same is not said about the f-pawn in King Pawn Openings, and hence why Nf3 is played far more often on the first move than Nc3.
The chess.com opening calls this (1.Nc3) the "van Geet", while I have a book (by Sam Collins) that calls it the "Dunst". But for simplicity I'll call it the VG.
The Nimzowitch Defense is actually not bad, and black can have equality after 2.d4, and can transpose after 2.Nf3.
The VG is simply the same as the Nimzowitch, except a tempo up! And if you have an extra tempo, that's usually good, right?
Similar to the Bird's opening as a "faster Dutch", why isn't 1.Nc3 played more often, if it's just an "accelerated Nimzowitch"?