user33819: As we all know, in algebraic notation, we usually suppress the notation for pawns. That is, unless they are capturing something. Then, for some reason, we must notate the file of that pawn. For all other moves, you only need to notate the file (or rank, or both) if multiple pieces of the same kind could move to the field in question, so that this extra information is necessary to avoid ambiguities.
For instance, the Scandinavian defense usually goes something like 1. e4 d5 2. exd5. Why not just 2. xd5?

user33819: Just realized one other good reason: When using this notation, it’s easier to get an overview of the pawn skeleton of the field solely from looking at the algebraic notation. For instance, to find out where the e-pawn is, you can look for the move starting with an e. That would be e4 in this case. Next, you find the next one, which is exd5. Then you make a mental note that the e-pawn has moved to the f-file. Now you can keep following it as it advances along this file, until it maybe changes file again. And so on.
It doesn’t offer much help in figuring out which pawns have been captured, but at least it helps.

user4418: 
Why not just 2. xd5?

Because we always indicate the piece being moved. The notation 2. xd5 doesn't tell us which piece is doing the capturing. We have to work that out for ourselves. We don't need to write 1. e2-e4, although we can, because 1. e4 tells us the e pawn is the one being moved.
For instance, in Petrov's Defence we don't write 1. e4 e5 2. Nf3 Nf6 3. xe5. Instead we indicate the piece being moved by 3. Nxe5.

user21223: I'd suggest a different reason: to make it sound natural.
How would you pronounce Nxe5? I would say "knight takes e5". In that case, the putative pawn move "takes d5" would not sound natural, because it has a verb with no subject.
Once you decide to add a "subject", you may as well do so in a way that gives extra information, since this may be useful. So rather than "pawn takes d5", it makes sense to say e.g. "e takes d5".
There is no grammatical reason to add this information to other captures (which already have a subject) or normal moves (which have no verb).

user33754: Imagine a situation where there is also a white pawn on c4, for example 1. e4 d5 2. c4 e6 3.xd5. You would have no way of knowing which pawn took on d5, was it the one on e4 or the one on c4.

user924: There is no real reason, it's not technically necessary.
Equally, you don't generally have to write the 'x'. Knowing where the piece is going is enough to know that it's a capture.
People must have thought this notation hit the sweet spot between maximum terseness and readability.

user12189: You seem to want the notation to be as efficient as possible, disregarding ease of use. Let's take this to extremes:

If White only has a single move or capture that ends on c4, then instead of Bc4 or Bxc4 should we just write c4?
If White only has a single legal Rook move, then instead of Re5 should we just write R?
If White only has a single legal move, then...what? Just notate it as "" ?

The conventions in use are a compromise between efficiency and ease of use. And they work very well.

33819: <p>As we all know, in algebraic notation, we usually suppress the notation for pawns. That is, unless they are capturing something. Then, for some reason, we must notate the file of that pawn. For all other moves, you only need to notate the file (or rank, or both) if multiple pieces of the same kind could move to the field in question, so that this extra information is necessary to avoid ambiguities.</p>
<p>For instance, the Scandinavian defense usually goes something like <code>1. e4 d5 2. exd5</code>. Why not just <code>2. xd5</code>?</p>
 33819: <p>Just realized one other good reason: When using this notation, it’s easier to get an overview of the pawn skeleton of the field solely from looking at the algebraic notation. For instance, to find out where the <code>e</code>-pawn is, you can look for the move starting with an <code>e</code>. That would be <code>e4</code> in this case. Next, you find the next one, which is <code>exd5</code>. Then you make a mental note that the <code>e</code>-pawn has moved to the <code>f</code>-file. Now you can keep following it as it advances along this file, until it maybe changes file again. And so on.</p>
<p>It doesn’t offer much help in figuring out which pawns have been captured, but at least it helps.</p>
 4418: <blockquote>
<p>Why not just <code>2. xd5</code>?</p>
</blockquote>
<p>Because we always indicate the piece being moved. The notation <code>2. xd5</code> doesn't tell us which piece is doing the capturing. We have to work that out for ourselves. We don't need to write <code>1. e2-e4</code>, although we can, because <code>1. e4</code> tells us the e pawn is the one being moved.</p>
<p>For instance, in Petrov's Defence we don't write <code>1. e4 e5 2. Nf3 Nf6 3. xe5</code>. Instead we indicate the piece being moved by <code>3. Nxe5</code>.</p>
 21223: <p>I'd suggest a different reason: to make it sound natural.</p>
<p>How would you pronounce <code>Nxe5</code>? I would say &quot;knight takes e5&quot;. In that case, the putative pawn move &quot;takes d5&quot; would not sound natural, because it has a verb with no subject.</p>
<p>Once you decide to add a &quot;subject&quot;, you may as well do so in a way that gives extra information, since this may be useful. So rather than &quot;pawn takes d5&quot;, it makes sense to say e.g. &quot;e takes d5&quot;.</p>
<p>There is no grammatical reason to add this information to other captures (which already have a subject) or normal moves (which have no verb).</p>
 33754: <p>Imagine a situation where there is also a white pawn on <code>c4</code>, for example <code>1. e4 d5 2. c4 e6 3.xd5</code>. You would have no way of knowing which pawn took on <code>d5</code>, was it the one on <code>e4</code> or the one on <code>c4</code>.</p>
 924: <p>There is no real reason, it's not technically necessary.</p>
<p>Equally, you don't generally have to write the 'x'. Knowing where the piece is going is enough to know that it's a capture.</p>
<p>People must have thought this notation hit the sweet spot between maximum terseness and readability.</p>
 12189: <p>You seem to want the notation to be as efficient as possible, disregarding ease of use. Let's take this to extremes:</p>
<ul>
<li>If White only has a single move or capture that ends on c4, then instead of Bc4 or Bxc4 should we just write c4?</li>
<li>If White only has a single legal Rook move, then instead of Re5 should we just write R?</li>
<li>If White only has a single legal move, then...what? Just notate it as &quot;&quot; ?</li>
</ul>
<p>The conventions in use are a compromise between efficiency and ease of use. And they work very well.</p>
