The ½ comes from an integration. Whenever you see a square term in an equation, there's often a corresponding ½.
Yes, we could "simplify" equations by getting rid of the ½ and squashing it into the units, but at that point, all of the stuff makes less sense.
I do physics with kids, and often show area (usually of a triangle) as the distance traveled with constant acceleration, the energy of something, the accumulated debt or what-not. The source of the ½ is very obvious -- we're looking at a triangle and not a rectangle.