3e destroyed this balance above about 4th level
In my experience, non-casters are quite effective above 4th level in 3e.
As a player, my paladin hit just about every time (to hits above 20 were routine) and did damage at least in the teens every round. The arcane casters' players sometime complained about it. Along with the Ranger, he did a lot of killing that got done, albeit often buffed.
The one head-to-head fight he had with a Wizard, he got initiative and killed the Wizard with one Smite Evil crit, before the Wizard could take an action. It helped that they were talking in a room at melee distances when suddenly things turned violent.
As to your other comment about 3e being too complicated and slow at higher levels, I agree. Above 13th level is where 3e combat becomes more paperwork than fun, in my experience.