4...Bb4 or 4...Nf6 are both good for Black. Non-symmetrical placement of the pieces can lead to Black getting a good game in the Exchange French.
For example if 4. Bd3 Bd6 5. Nf3 Ne7! Perhaps if White castles kingside, it could be advantageous for Black to castle queenside.
I've won the great majority of my OTB exchange french games as white. They aren't complex positions, and are often roughly equal for a long time, but there will be winning chances at least at my level (mostly facing 1700-2000 crowd). White needs to be willing to press in the endgame though.
I like 4.c4
I (you) know that it's statistically a drawish position, but at least a game has to carry on, right!?. Since it's white turn to continue, presumably white responds with 4.Nc3 attacking black d5 pawn, what would be the continuation for black?
*PS : Internet mostly doesn't discuss the exchange variation, I assume because it's going to be a boring game for both sides (draw).