QGD - 3...Bb4

Why do we see 3...Bb4 so infrequently?

After 1. d4 d5 2. c4 e6 3. Nc3 Bb4

Those are reasons to play this move -- but my question is: then why do we see it so IN-frequently?

Right . . . my question is: why is it not a popular line?

It is supposed to be a bit premature after 4.a3 or 4.e3, but things are far from clear- personally I think it's a good move, and quite suitable for defending against 1.d4 with the Ragozin regardless of white's third move.

I guess because many players don't see much upside in using this move order. It's less flexible because in some Nimzo lines it's not ideal that Black has already commited to d5.

Compared to the Nimzo 4.a3 Bxc3 bxc3: Black usually doesn't play d5 and tries to create counterplay against White doubled c-pawn. Here White can easily get rid of his doubled c-pawns.

Compared to the Nimzo 4.f3 d5 a3 Bxc3 bxc3: Here White can make a more useful move than f3

However, it is certainly playable

It gets recommended every once in a while.  "The Complete Ragozin" gives a bit more detail about it as a way to get to the Ragozin proper or even to avoid the classical/Rubinstein lines of the Nimzo.

There are openings where the d pawn goes to d6 or d5.

There are openings where the bishop goes to b4 or e7.

But in (practically) every opening the knight goes to f6... so playing a move (like Bb4) that helps define the opening gives your opponent more information and limits your options, meanwhile Nf6 during the first 3 moves does neither of those things.

Qa4 is pretty common in the Ragozin. After Nf6 and Nf3 you reach a well known position where the white queen may not be ideally placed.

Is it "inferior" to the point that it's "refuted"?  No!  Nothing has been shown to refute 3...Bb4.

However, like many other openings, there are many lines where the addition of a move by each side or lack thereof makes a difference, one way or the other.

For example, The Vienna Gambit with Nc3 and ...Nc6 is supposed to be slightly better for White than the King's Gambit (1.e4 e5 2.Nc3 Nc6 3.f4 compared to 1.e4 e5 2.f4).

The Queen's Indian Defense (1.d4 Nf6 2.c4 e6 3.Nf3 b6) is viewed by most at the top level as more sound than the English Defense (1.d4 e6 2.c4 b6), where again, the difference is having committed to Nf3 and ...Nf6 vs not (same difference as the line the OP posts compared to the Ragozin proper).

I do not claim to be any type of expert at the Ragozin as it's not part of my repertoire from either side, but you need to look into the differences between the line you propose and the same line with both sides having committed to the extra Knight move, and which side it benefits that neither side can advance their f-pawn.  I am going to guess, based on frequency of occurrence at the GM level, that the addition of Nf3 and ...Nf6 likely favors Black slightly, not that the position itself favors Black, but comparing 1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.Nf3 Bb4 to 1.d4 d5 2.c4 e6 3.Nc3 Bb4, the former is likely a slight improvement for Black than the latter, but I am only basing this on frequency of occurrence at the GM level, and do not claim to be an expert at this specific line.

It might avoid the classical Nimzo, white playing Qc2 would be gambiting the c-pawn, but not the Rubinstein. A few books on the Ragozin, like Pert's, cover this move order.

          It could be quite useful against d4 players who tend to look for safe structures familar with, rather than concrete lines.

@TwoMove Cornette refers to the Nge2 lines, you should read his book if you want to learn more.

@ThrillerFan one of the benefits of having a knight on f6 is for a quick Ne4