I think giving weapon damage a type is smart. In 4e, resisting weapon attacks wasn't simple, usually it became resist all, or specifically ranged/melee or calling out weapon attacks...blah. I like weapons having a type of damage.
I'm less thrilled about weapons having three separate damage types. B/P/S makes sense, and I agree that they are very different if you ever get to experience them first hand, but unless its a benefit to the player to have three different types, I don't like it. If the only thing weapon damage types gets used for is "your bow sucks against skeletons" then its not a good core mechanic. Even if there is the occasional "your bow is good against the pin-cushion-beast" you'll find yourself punished more often than not, and then, BPS is a liability.
With other damage types, there is a viseral reaction to them, A fireball, a lightning bolt, ray of frost. You can get behind them in your immagination, and even if everything resists fire, you still want to play a pyromancer. If your cone of cold can freeze a salamander, but my scorching ray does half damage, I can buy that. But when my sword can't smash a skeleton, but your stupid club can, I don't care about cutting edge or trained technique or what-not, my three feet of steel has enough momentum to bludgeon with the best club out there.
So, unless BPS will get some real support/fun/advantage for players, I would rather just have "physical" damage, and be done with it.