The first thing I want to say is that this isn't intended as a troll post QQing about how much better melee dps is. Blizz has come a long way in balancing classes and making different fights more friendly towards melee or caster from fight to fight.
The problem I have with melee dps is how much damage is "given" without doing anything. Using Recount on my warlock for example, my top 3 damaging abilities are, incinerate, Chaos Bolt and Immolate. All 3 require constant casting, even if that does mean spamming incinerate.
Melee Dps (and Hunters) almost always end fights with their top damaging ability being auto-attack. That means around 1/3 of their dps is given to them by right clicking on the enemy at the beginning of the fight.
What this all means is if a melee tops the charts at the end of a fight with 10k dps and a caster is second with only 8k then the melee seems to have "done" more dps. In all actuality though the caster has done 8k while the melee has only done about 6.7k (10k-1/3 of 10k)
Now this is how Blizz has made the classes balanced, so even though allowing casters some "free" dps would be logical it would make casters OP since they would become unbalanced. In my opinion melee should have to at least click a button to melee so they arent given so much of their damage with 0 effort.