This suggestion would reduce randomness, true, but would probably make combats incredibly boring. Doing a constant small amount of damage as your whole turn just sounds tedious, especially against enemies with high HP. You can't compare 5e fights to DOS fights, because in DOS each characters gets multiple actions per turn and there is such a greater ability for combos (surfaces, stunning, etc) in DOS. These things just aren't that prevalent in 5e.
The "use average damage rolls" alone (as an option) is fine. That's a commonly used option for monsters in PnP 5e.
Reducing damage by the %-chance to miss is meh. It will make all characters feel less powerful and also will have cascading effects on concentration, attack effects like "poisoned if hit by an attack", etc. If you want to reduce the chances of missing, better options are probably:
-weighted d20 (either making higher numbers more likely, or "storing" past rolls so you can't roll a # again until you make 10ish more rolls)
-a flat enemy AC (and ST) nerf in lower difficulties.
