Why can't people just play an ordinary elf, halfling, gnome, dwarf or human?
Oh thats simple ...
Same reason Elves, Dwarves, Halflings and Gnomes were even invented ... Humans are common, therefore they are boring for many people ...
So we get someting rare, something exotic ... Elves, Dwarves, Halflings and Gnomes ...
But in time, they become so common, so they get boring. :P
And the wheel of time keep turning.

Yuan-Ti are monsters for a reason, same as goblins, kobolds and every other monster race someone may ask to play.
I highly doubt we would be able to agree on what that reason even is.

Or what it even mean to "be a monster" ...
But i dont think that would change anything. :-/
Look at Drizzt Do'Urden ... he was (as it seems to me) to be the only Good (or at least not-Evil) Drow ...
We all know that in fact he was just first one, that was inevidable.

But Drows as a race are still concidered Evil ... so what actualy changed? And i mean in setting, not in particular games.