It has been played, but has never been popular. Basically speaking, the bishop is very passive on d2, you will have to move it again soon or later. Also the move does nothing to pursue white's strategic goal of pushing the e pawn to e4. Among others, black might play 4...d5, with a sort of QGD where white has played a suboptimal bishop move (black is even threatening 5...dxc4/6...Qxd4 due to the bishop interfering with the queen; of course the threat can be stopped but this just shows how Bd2 is doing white more harm than good), or just wait with 4...0-0. Then if 5.a3 black can play either 5...Be7 (the "loss of time" Bf8-b4-e7 is totally compensated by the fact that white will also need to move the bishop again, and the extra move white has gained in the process is the hardly exciting a2-a3 push. So the tempo count is actually favourable to black) or 5...Bxc3. After 6.Bxc3 Ne4 7.Qc2 f5 black can regain the bishop pair at will and has reached his strategical goal of conquering e4. He is at least equal.
4.Bd2 is hardly bad or dubious, but still unchallenging and needlessly passive. That said, as an occasional surprise weapon it has been played by very strong players (I think even Petrosian gave it a go).
In this opening, after 1. d2-d4 Ng8-f6 2. c2-c4 e7-e6 3. Nb1-c3 Bf8-b4, Why doesn't white play 4.Bd2?