But you would not get the perks. Some are really worth the title of perk. Like stepping on a trap and not setting it off (under sneak skill).
I just have to say that of all the perks that are useful, that would not have been one I would have listed. I generally just walk around traps.
For the OP there is nothing BETTER about playing the at level one other than maybe saying you did it. The perks are fun, why exclude them from your play just to not level? Sure creatures get tougher as you level, but your a good player right?