The matter of Bf1-d3xc4 is only a matter of one tempo difference. Your logic is spot on, but Black obtains good positions from the QGA for other reasons. Notice that in the position you presented, FromMuToYou, ...c6 and ...e6 are slight concessions. Black achieves ...c7-c5 often in the QGA. As far as 3 e4, that move, although aggressive, is loosening for White. Black has countermeasures and White is better off playing e2-e3 in such formations.
The QGA is quite effective.
So couldn't you play the Orthodox line to preserve the c7-c5 break without accepting the pawn until the bishop moves? Can you post a concrete variation where something is gained from accepting immediately?
Every line involves concessions of some kind. In the Orthodox line you mentioned White will use Bg5. White vs the QGA in playing e2-e3 shuts in his dark squared bishop. 1 d4 d5 2 c4 dxc4 3 Nf3 Nf6 4 e3 e6 5 Bxc4 a6 6 0-0 c5 could serve as the QGA line to discuss.
Part of your confusion stems from the fact that this isn't a QGA. It's a semi-Slav. This, of course, is a pretty pure semi-Slav, based on the move order. That retains that classic Caro-Slav pawn structure and allows its characteristic mid-game pawn breaks by black.
In a QGA, because of the tempo difference, you don't get that same sort of structure. Yes, white gets the pawn back without deploying the bishop elsewhere first, but as recompense, black generally gets in ...e5 or ...c5 in one go, allowing a far more open game that allows quicker development to more classically "optimal" squares, and less of a slow-developing, strategic game that will erupt in midgame fireworks (a la the semi-Slav).
With those swift central thrusts from black, the center tends to liquidate swiftly in QGA's, and wide open games with piece play are good for neutralizing white's offense at high levels of play...but perhaps not quite so good at giving yourself a chance to organize a counterattack if your aim is to play for the full point as black.
Both good openings, but play very differently, and usually with different strategic goals in mind.
I know the diagam is a semi-slav. My curiousity was about the QGA but I started off with the that line from the Semi-slav because I wanted to clearly illustrate the idea of dxc after the LSB moves. So your claim is that black captures immediately to save time in a different way achieving c5 or e5 in one move. First of all I find it hard to believe black can ever manage e5 in any line where white is not asleep (I'm excluding the 3.e4 lines because I think that's a completely different beast.) I don't play either side of the QGA, or even the queen's gambit, but I can't imagine where black is under so little pressure as to get in a very ambitious e5 break. It can't be disputed that black will save time with a c7-c5 break in the QGA relative to the Slav or semi-Slav. But the thing is black seems to retain that same exact advantage in the Orthodox line. Now that I skim through Orthodox mainline variations I think I found what I was missing before. In the Orthodox variations black is discouraged from playing ..c5 for positional reasons. In the Tarrasch black can and does play ..c5 as early as move 3, but in doing so is accepting a permanent positional weakness in the form of an isolated queen's pawn. And if that opporunity is not taken to play c5, white will undoubtedly play Bg5 where c5 is even worse. Black's DSB is really needed on Be7 and just not doing much on Bc5. And after ..c5 dxc capturing with a piece other than the bishop doesn't seem practical at all.
So that about solves this mystery for me.
Now that KG's are involved, I have to assume you have no idea what opening you've posted, nor which you're asking about.
The info I gave on the semi-Slav pawn structure is real, as is the info on breaks in the QUEEN'S gambit accepted, and the differences render your question sort of nonsensical. (...e5 is the most common move 3... in e4 QGA lines, and the second most common move -- and the best, IMO -- in e3 lines, and c5 is the most common move 5... in the Nf3 lines.)
I hope you figure these things out, since the average 1000 in my club has them down pat. That you're apparently expert strength and haven't yet puzzled it all out leaves me scratching my head about the ratings on this site.
Seems I'm trying my hardest to confuse you lol.
I edited it. (I do wonder though, you really couldn't gather from context that I'm not talking about the King's gambit here? 
)
Well, I AM confused. Surely without 2 ... dxc it's not a QGA?
The QGA's I play as Black never resemble anything like your final position. (And because I'm still trying to learn it, I follow DB moves for quite a long way)
Now that KG's are involved, I have to assume you have no idea what opening you've posted, nor which you're asking about.
The info I gave on the semi-Slav pawn structure is real, as is the info on breaks in the QUEEN'S gambit accepted, and the differences render your question sort of nonsensical. (...e5 is the most common move 3... in e4 QGA lines, and the second most common move -- and the best, IMO -- in e3 lines, and c5 is the most common move 5... in the Nf3 lines.)
I hope you figure these things out, since the average 1000 in my club has them down pat. That you're apparently expert strength and haven't yet puzzled it all out leaves me scratching my head about the ratings on this site.
I am going to advise the guys in your club rated 1000 to drop the opening encyclopedias and pick up a book on tactics. I bet they hit 1200 in 2 months.
Well, I AM confused. Surely without 2 ... dxc it's not a QGA?
The QGA's I play as Black never resemble anything like your final position. (And because I'm still trying to learn it, I follow DB moves for quite a long way)
It's confusing because I keep jumping back and worth between the QGA, the Slav, and the Orthodox. I'm doing so because I'm comparing them since they all have the same dxc and potential c5/e5 breaks in common. In general the positions have a lot of similarities.
The diagram is actually semi-Slav. It's only the diagram because it's basically the most common mainline in my DB and I wanted to show the late dxc after white has moved the bishop.
So this is the most common opening sequence played in master games after 1..d5
What I want to discuss is the c4-d5 tension. For 8 moves both sides ignore it. I think the reason is pretty simple: whoever captures gives the other side some kind of advantage. If white captures, black can recapture in a way that only frees up his game and provides more space to develop his pieces. If black captures, white can recapture with the bishop thus a tempo is lost for black. The veteran Queen's gambit player understands this which is why he procrastinates developing the LSB for a bit. So in the line I've shown after 7.Bd3, black finally decides to capture to force white's LSB from Bd3 where it is very strong to the weaker c4 where it stares at the solid e6-f7 pawn chain, knowing he will not lose time in the process because the bishop has already moved.
This is the theory as I understand it. But perhaps I am mistaken somewhere because 2..dxc (QGA) is quite popular even at the highest level and seems to score just as well as 2..e6 or 2..c6 Using the same reasoning as above, white can now move the e pawn and capture with the bishop with no time lost. Not only that, but black has even allowed white 3.e4 if he wants it. If grandmasters are playing this I must be missing something.