PVP would work easily in D3, there is plenty of proof of that. they even made arenas and had a TvT mode like others mentioned, balancing wouldnt be hard. all they have to do is have everyones stats who enter arena be fixed and set the same for everyone, lots of games take this approach and seems to work for them.
the bottom line is they realized eventually they would not only have to update the game with PVE stuff they would have to cater to the PVP crowd also. causing even more content to be made and with such a small crew still working on D3(why do you think there was no announcement of an expansion at blizzcon?)it would take too much time and resources and take away from the PVE content.
So in short they decided to scrap all the PVP stuff they were working on and just focus on the PVE stuff.