As far as I am aware, in Harry Potter, a wand is simply a means of channelling magic.
In Harry Potter and the Deathly Hallows, at Malfoy Manor, Harry grabs three wands from Draco and performs a triple-spell on his enemy. The force of the triple spell wasn't divided by three. Instead, the books mentions that it was multiplied by three.
Thinking about it, he increased his magical power by channelling it through not one but three wands simultaneously. If this can be done by wands, why didn't wizards think of congregating wands into one single powerful tool? Or maybe using some special Wand-like tools to increase channeling of magic through a Wand?
I'm not sure if what Harry did was a pure accident but had I seen this effect produced by three wands then I think I'd have bound multiple wands together with rubber tape.