I started out not using a wand. I like the way I casted spells without a wand. When you can use wands that give you a pip or power pip then it is foolish to not use one. The other reason I did not use a wand (levels 6-12ish) is that the wand taps, or bonks as we call them, took up space in my deck and I want not as adept at deck management as I am now. Of course, I do not use wand taps now much, as that can draw aggression.
Sometimes people don't use wands (and can include heir athames, amulets, rings) because of all the sideboard spells. They want to get straight to the regular spells. This can be good for mobs, especially at the 20-40 levels.
At really low levels, wands are essential, as you wouldn't have much else to attach with, and the wand spells help. At much higher levels, the wands give extra boosts that are also essential.
There are times at mid-levels when I don't use a wand, simply because I don't need the wand hits.
I only start using wands once they start offering the additional pip.
The reason I don't use wands before that is because I have no need for the level 0 wand spells. Actually, you could think of it as cluttering your deck. Yea, you only have like 5-7 wand attacks, but, still, that eats into your cards that you would normally 'want' to have over wand attacks.
Even now, I rarely ever use my wand to attack. I may attack with my wand out of random when I have no blades/traps/bubbles/spells to cast on my turn. But even then, I discard any other wand attacks, and all future wand attacks if I don't intend to use them on that same turn.
But there is an advantage to using a wand. As a level 34 Pyromancer I own several - one for each school. And I will only use the ones with sparklers attached, not the ones with cards. Here's how I use it for advantage. If I'm facing another fire wizard I use my ice wand or life wand. Usually ice because it gives me pips right at the start. The sparklers cost you nothing to cast so you lose no pips. When a guy's down to 40, blast him with some snow and be done. I don't use my fire wand because it will break my casting blade before I'm ready to use it. Look in the bazaar. When the description card comes up as you mouse over a title, it will say that it gives you pips or not at the start of your duel. That's the one you want. Happy casting!!
In the first few worlds, enemies do not commonly use shields, or at least not as much as later on. I didn't use a wand because I could never find one I liked, I always got hands with all wand cards on the first turn, and I saw no immediate use. Now I use a wand, since I can break Storm shields.
These players are playing with quite small decks containing only a few key spells, so they can always cast those spells when they want to. Not using a wand means that the bolt spells a wand gives don't dilute what they want to cast.
Many lower level wizards choose not to use wands because those wand spells use pips that are better used for primary school spells. Keep in mind that most lower level gear boosts primary school attacks, so your deck spells have more power than wand attacks. At higher levels, however, wands are very useful to boost pips, critical and block stats, as well as breaking tower shields, without using pips.