Have you noticed how central they are to the book in other ways? They are the defining aspect of wizardry, they become the symbol of the oppression of other magical creatures, as goblins are denied wands, and they are taken from muggles as a symbol of their magic, and they are accused of stealing them from wizards as a way of taking magic.

Now, if I can be forgiven an allusion to Freud in all this (seriously, it is a wonder we have managed to discuss a book with wands without stumbling across him every couple of pages), the wand as a phallic symbol of power is really very, very clear.