There's also a bit of slippery-slope of rules development to consider. Assume, for the moment, that hit points by level are fixed per class. Well, might as well do that for monsters, too, right? Then, there will be the pressure to make damage a fixed thing as well (since it is measured against known hit points, this leads to more mathematically sound balancing). And, of course, there's already point-buy stats. So, now we have standardized stats, hit points, and damage. Why, precisely, would we want to keep random to-hit, saves, and skill checks? Why not just go diceless and be done with it?
At some point along the way, you realize that there is some point to randomness in the game. All that remains is a decision as to where to draw the line between fixed progressions and randomness.