IMO... Not played because White's main advantage against the Center Counter Defense (especially in the Anderssen 3...Qa5) relies on "TRYING TO" take advantage of Black's lack of development.
4.a3 does nothing.. Black will just develop with something like 4...c6. and be ahead of where he/she normally is at after that move.
As someone who plays the Center Counter defense regularly (I'm a club level player, so take my opinion at that value) My opinion :
Both White and Black are in a development race to get through the door to the middle game, if Black get's through first, Black has a good game, if it's tie... Black fights for a draw... If White get's through the door first, baring a blunder by White, Black looses.
That's my rough opinion.
You also have different lines, where you have to know what your walking into ;
Example 8. Nd5 or 8. Ne4 are the current trend, both transpose into the same position ... People think "Oh yea I have doubled the pawns. White is better. Not really...... both moves transpose into Bronstien-Larsen variation in the Caro-Kann .... Which gives Black the attacking initiative on the kingside using the open g file.. (at my level, I score a lot of wins from that position) Nothing wrong with those two moves ... just the play from the position (the counter attacking by Black) is not what many expect at my low level.
I've been looking for some openings against the Scandinavian, and I saw stockfish suggesting me 4 a3 after 1e4 d5 2 exd5 Qxd5 3 Nc3 Qa5. It seemed like a good way to play against the Scandinavian but I don't get why it's so unpopular.