user18842: Why is typical move order for QGD among top grandmasters 1. d4 Nf6 2. c4 e6 3. Nf3 d5? Why does not black immediatelly go 1. ..d5?
Also, why is QID via 3. ..b6 almost never played?

user3594: There is no real objective answer, both are playable at any level. Such variations in move order are decided primarily according to roughly 3 common criteria:

a) Comfort zone of the player: which structures they're more familiar with, and therefore, they may opt for lines that maximise the liklihood of ending up in those. 
b) The types of variations and transpositions they want to prevent from occurring (depending on the opponent), which itself depends on various elements.
c) The kind of game they've envisaged: double edged, conservative, etc. (this is a subcategory of b) essentially), all of which influence how committal you're going to be with your starting moves.

Therefore, these matters tend to be quite opinion-based, that said, here's an attempt to shed some light on a handful of key differences between the two specific lines: 

More particularly for the line you ask about, 1.d4 Nf6 2.c4 e6 3.Nf3 d5 ... often called the anti-Nimzo qualifies as one of the most versatile options for black as there still remain a diverse set of variations for black to consider, to name a few (assuming 4.Nc3):

On the solid side: 4...Be7[*] (leading to mainline QGD with Bf4...e3).
Or sharper variations such as: the Vienna 4...dxc4
Tarrasch 4...c5
Ragozin 4...Bb4

Note that white is also keeping many options open with 3.Nf3 instead of Nc3.
On the other hand, with 1...d5, well for starters, Nimzo Defence options are essentially ruled out, and assuming black is going to follow with e6...Nf6, white is left with early options to divert towards fundamentally different structures such as the exchange variation of the QGD: 1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.cxd5 exd5 5.Bg5 ..., compared to the move order with 1.d4 Nf6 2.c4 e6 3.Nf3 d5 where an attempt to transpose to an exchange variation with 4.cxd5 exd5 leads to poorer version of that system for white as the early Nf3 is almost a lost tempo since black has to pressure d5 (with early Nc3 and Bg5 pinning f6-defender) while including an early Qc2 to prevent black from creating a good light-square bishop with Bf5.
So the whole setup with early Nf3-cxd5 and without Nc3 allows only for a nonthreatening transposition to the QGD exchange variations.
Instead, by not committing to d5 [**] on the first move and playing Nf6, black preserves the option of playing the Nimzo among other lines (and therefore, avoid QG's altogether if so desired), while transpositions to most variations with pawn on d5 remain open, which leads us to the natural conclusion that: not making early committal pawn moves in the centre tends to leave us with more options on the table. 

So as you see, all these lines are possible but the decisions are made according to one's preferences (and the circumstance at hand) and neither option (1...d5 , 1...Nf6...) is generally better or worse.
Regarding your last question,

Also, why is QID via 3. ..b6 almost never played?

it's not clear what you mean, the move 3...b6 is the defining move of the Queen's Indian Defense (QID), and it is frequently played (by e.g. Carlsen, Karjakin, Anand, Ivanchuk, ...).
[*]: This mainline followed by Bf4..e3 and 6...c5 also happens to be what Carlsen - Caruana had prepared for during the recent world championship event, see e.g. game 7.
[**]: Similarly, 1...d5 also avoids certain lines that 1...Nf6 doesn't, but there's not enough time/space to get into that. 

18842: <p>Why is typical move order for QGD among top grandmasters 1. d4 Nf6 2. c4 e6 3. Nf3 d5? Why does not black immediatelly go 1. ..d5?
Also, why is QID via 3. ..b6 almost never played?</p>
 3594: <p>There is no real objective answer, both are playable at any level. Such variations in move order are decided primarily according to roughly 3 common criteria:</p>

<ul>
<li>a) Comfort zone of the player: which structures they're more familiar with, and therefore, they may opt for lines that maximise the liklihood of ending up in those. </li>
<li>b) The types of variations and transpositions they want to prevent from occurring (depending on the opponent), which itself depends on various elements.</li>
<li>c) The kind of game they've envisaged: double edged, conservative, etc. (this is a subcategory of b) essentially), all of which influence how committal you're going to be with your starting moves.</li>
</ul>

<p>Therefore, these matters tend to be quite opinion-based, that said, here's an attempt to shed some light on a handful of key differences between the two specific lines: </p>

<hr>

<p>More particularly for the line you ask about, <code>1.d4 Nf6 2.c4 e6 3.Nf3 d5 ...</code> often called the anti-Nimzo qualifies as one of the most versatile options for black as there still remain a diverse set of variations for black to consider, to name a few (assuming <code>4.Nc3</code>):</p>

<ul>
<li>On the solid side: <code>4...Be7</code>[*] (leading to mainline QGD with <code>Bf4...e3</code>).</li>
<li>Or sharper variations such as: the Vienna <code>4...dxc4</code></li>
<li>Tarrasch <code>4...c5</code></li>
<li>Ragozin <code>4...Bb4</code></li>
</ul>

<p>Note that white is also keeping many options open with <code>3.Nf3</code> instead of <code>Nc3.</code></p>

<p>On the other hand, with <code>1...d5,</code> well for starters, Nimzo Defence options are essentially ruled out, and assuming black is going to follow with <code>e6...Nf6</code>, white is left with early options to divert towards fundamentally different structures such as the exchange variation of the QGD: <code>1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.cxd5 exd5 5.Bg5 ...</code>, compared to the move order with <code>1.d4 Nf6 2.c4 e6 3.Nf3 d5</code> where an attempt to transpose to an exchange variation with <code>4.cxd5 exd5</code> leads to poorer version of that system for white as the early <code>Nf3</code> is almost a lost tempo since black has to pressure <code>d5</code> (with early <code>Nc3</code> and <code>Bg5</code> pinning <code>f6</code>-defender) while including an early <code>Qc2</code> to prevent black from creating a good light-square bishop with <code>Bf5.</code>
So the whole setup with early <code>Nf3-cxd5</code> and without <code>Nc3</code> allows only for a nonthreatening transposition to the QGD exchange variations.</p>

<p>Instead, by not committing to <code>d5</code> [**] on the first move and playing <code>Nf6</code>, black preserves the option of playing the Nimzo among other lines (and therefore, avoid QG's altogether if so desired), while transpositions to most variations with pawn on <code>d5</code> remain open, which leads us to the natural conclusion that: not making early committal pawn moves in the centre tends to leave us with more options on the table. </p>

<hr>

<p>So as you see, all these lines are possible but the decisions are made according to one's preferences (and the circumstance at hand) and neither option (<code>1...d5</code> , <code>1...Nf6...</code>) is generally better or worse.</p>

<p>Regarding your last question,</p>

<blockquote>
  <p>Also, why is QID via 3. ..b6 almost never played?</p>
</blockquote>

<p>it's not clear what you mean, the move <code>3...b6</code> is <strong>the</strong> defining move of the Queen's Indian Defense (QID), and it is frequently played (by e.g. Carlsen, Karjakin, Anand, Ivanchuk, ...).</p>

<p>[*]: This mainline followed by <code>Bf4..e3</code> and <code>6...c5</code> also happens to be what Carlsen - Caruana had prepared for during the recent world championship event, see e.g. game 7.</p>

<p>[**]: Similarly, <code>1...d5</code> also avoids certain lines that <code>1...Nf6</code> doesn't, but there's not enough time/space to get into that. </p>
