Because it's useless. Press pause and the difference with stop is none.

Pause pauses the current song being played but keeps it open for
access (I believe).  Stop stops the song playing and selects nothing,
effectively "wiping the board clean".

0 difference to the eye.

I don't see any bug report here.  You just mention that you believe
that  pause keeps the song "open for access".  It doesn't.

And what is the use in "wiping the board clean"?  

If you want this reopened, please carefully describe a scenario in
which having a stop button would solve some actual problem.

1. This was submitted as an interface improvement.  Hence, it is a
suggestion.

2. Saying there is no need for a Stop button is like saying there is
no need for a Stop button on a VCR or DVD player.

3. Considering every other audio player I have seen out there, whether
it is a piece of software like XMMS or a MP3 player like a Rio or a CD
player, they all have a Stop button.  Some users might get confused
that there is no Stop button, as more non-geek people move to Linux.

4. I was unsure of how RB handles files, in my programming experience,
you have to open a file and keep it open to work with it.  (Such as
simple things like text files and .wav files.)  This makes the file
unusable to any other program until it is closed by the program that
has it opened.  As you mentioned, that is not the case with RB, so I
am mistaken.

*** Bug 152519 has been marked as a duplicate of this bug. ***