I only play The QGA against The QG,I really don't know any theory, but my results are decent (-3).I'm sure I'd do much worse if I played anything that required sophisticated use of pawns. I just want to get my pieces out fast.
Why isn't the Queen's Gambit Accepted more often?
it's harder to combine it with another opening to form a coherent repertoire against 1 d4. so for example, if your goal is to take c4 in most cases you would rather choose the slav lines or semi-slav lines, because it is easier to combine it with other openings in case white doesn't allow you dxc4. one reason is that the semi-slav and slav already have structures in which you have d5 as a center pawn so there's no additional workload. with the qga you have to play something else if white delays c4 or avoids it altogether, and in that case you would be left with either a suboptimal sideline or a main line version of a queen's gambit declined which you could have chosen in the first place, or a different main line altogether which is yet another workload. however, the qga is good enough if your opponent only plays 1 d4 d5 2 c4.
another deterrent might be the very concrete nature of the entire line, which in itself would not be so bad, but if you had to learn something else to pair with it which might turn out to be also concrete it puts a lot of burden on the mind, which is unnecessary given there are simpler choices that are not worse.
maybe a third is the possibility of opponents catching up to your knowledge is a lot more likely in the qga, than in the qgd where there's a million main lines to choose from. at the start, it is a benefit to have a narrow forcing repertoire but eventually people are going to know what to do and that will become a liability which will force you to expand to something else.
that is my opinion. i don't play the qga, i have studied some of the lines albeit rather cursorily. i have played against it since i play 1 d4 2 c4. i think white has a more pleasant position in the endgame line and in the iqp line and i don't know if black can avoid both. maybe that is a fourth reason.

It's more principled to decline it.
dxc4 gives up a centre pawn for a flank pawn allowing white to take over the centre with e4. This is the purpose of white's move c4.
e6 and c6, maintain black's centre d5 pawn. This gives black more space and prevents white from playing e4.

Chess principles. Also, everyone tells them to decline it. You need to be careful if you play the QGA, while in the QGD, it's a quiet, boring game with no reason to worry or rush.
If you decline the gambit with e6, you commit to a solid center, prepare development and prepare to castle your king to safety after Nf6 and Be7. If you accept, you give the center and trade a center pawn for a flank pawn- which is a little bit unprincipled in an opening. You could argue that white trades a center pawn for a flank pawn in the Open Sicilian, a highly respected opening, but we don't talk about that.

Preference I guess but following 2…dxc4 with 3…e5 against almost everything except 3.Nf3 is a very strong choice and even recommended by Graham Burgess. I prefer the Semi-Slav though which tends to delay the exchange as I love the Botvinnik variation.
Also, some people want to build up the tension in the center and allow White the chance to fix it which most of the time from my experience can be bad for Black

Accepting it gives white a good claim in center if white wishes to. You don't even keep the pawn in more than most variations so declining is safer.

I see the vast majority of players above beginner level decline the Queen's Gambit. Is there a reason why? Black is completely fine if he accepts and has plenty of ways to play. It also could give you an advantage in theory if you know lines ahead of time.
It isn’t very principled, no? You move a piece twice in the opening to take away from the center to overextend a pawn that either forces you to overextend your queenside to protect it or allows White to take back in one move with the bishop, giving better development and a great center.

Who cares about principles, I play the QGA for the very reason others avoid it, it's a tough slugfest from the move 3 onward. I don't want to win the game, I want to beat my opponent, and those two things are not the same, not by a long shot. It's why, as black, I play 1...e5 to whites 1.e4, I want white to play their favorite line...and batter them down anyways.
The QGA is quite a decent opening, and even the strongest players i the world play it once in a while. There is no reason to avoid it
In several lines black´s pieces are cut off from the king side which can give white a nasty attack against the naked black king.

Ironically I actually defeated an IM that was conducting a simul. I was obsessed with the opening at the time and had read James Rizzitano's opening repertoire book on the QGA. Sure enough, the IM played every book moves James noted, and after that I played for a cheap tactical shot that somehow got overlooked by the IM. I won a piece for free and the IM resigned on the spot.
That said, I found the memorization to get there quite tedious, and at one point I lost a CC game when white went for the more aggressive e4 shot in the center. I got crushed off the board and quickly abandoned the whole QGA approach after that.
I think the QGA leads to a sort of static structure for black that is harder and less fun to play. It's actually a fairly boring opening for black. Also, I couldn't tell you how many times I have brought my bishop to c4 and then swung my queen to a4 and/or b3 and taken a huge advantage from it. I think many think my Qa4 is a mistake.

People make broad generalizations about the QGA for some reason but there are a bunch of layers within it.
It can be a "boring opening" if you play it the way 2750+ play it, but if you play like, 3. e4 b5 (w exchange sac) or even 3. e4 Nf6, combined with 3. e3 e5 (and maybe Nc6 on move 4 rather than taking on d4 which imo is more fun), and then some non-main line vs 3. Nf3 (most obvious example is 3...Nf6 4. e3 Bg4 but there are numerous other fun moves on move four) then there are plenty of ways to play for a win.
I'm pretty fond of it as a good opening vs 1. d4 and I don't see myself abandoning it anytime soon. It's possible within it I'll make changes, like I used to play 3. e4 Nc6!? and nowadays I've tended to prefer more solid moves, but the opening itself is a good one.
wrt op's question, it's just because I think most coaches are more comfortable teaching students to maintain the strongpoint on d5 rather than taking c4, because they are concerned that their students will just lose all control of the center and not know how to get counterplay. I can understand the argument that the QGA may be a better rec for like, 2000+ than it is for 1500 or below

3. e3, 3. e4, and 3. Nf3 are all about equally strong, they each have plusses and minuses but they all give white a little pressure for a bit and then of course black is fine with good play. I wouldn’t really say 3. e4 is particularly better than 3. e3, having played both and faced both countless times
I see the vast majority of players above beginner level decline the Queen's Gambit. Is there a reason why? Black is completely fine if he accepts and has plenty of ways to play. It also could give you an advantage in theory if you know lines ahead of time.