Thats not really the case. There is a one-handed and two-handed skill, so even if you don't have perks specializing in axe combat, you will still be better than a mage if your one-handed skill is higher.
Okay, I will explain further, although this has been said a few dozen times too often:
You have a warrior with maxed 1-handed weapon skill and a pure mage that never touched a melee weapon.
Now both pick up a 2-handed weapon.
In reality, one would expect the warrior to be better with it from the start, but this is not the case without attributes. Both characters are equally good or bad with 2-handed weapons, although the warrior is a melee weapon master.
And this doesn't even take hand-to-hand combat into account, which might get its own skill again because acrobatics and athletics have been cut. A boxer that picked up a sword would be just as helpless as a wimpy Bosmer hunter.
I really don't see how this is a bad thing though, there just eliminating one extra choice that is already made elsewhere. Sure, i can't speak for encumbrance, but your health/magicka/stamina are covered by leveling up those three "attributes". Its a little simpler, I'll admit, but whats the point of keeping something if it can be handled better in other ways. We can't say its handled horribly until we play the game.
I was just arguing semantics. I don't think "complex" is a word that describes the new system correctly.