*snip* Being in a higher position means you can shoot over their cover, or nullifying it completely depending on how high you are. This isn't only realistic, but is reflected in the rules as "Advantage". On a level plane, with the target behind a waist high cover, you have a smaller target than you would have if you were higher up. In the rules, it gives a +2 AC? This has the effect of making the target harder to hit, on a level plane. If you're higher up, you have a larger target, because the waist high cover might now only be knee high, depending on the range and angles. In game, this is reflected as advantage, and it should be clear to see why it is advantageous. This is the one thing I don't miss about table top, aside from when it's at my house, and I have to clean up the next day, rules lawyers, and it's especially bad when they're lawyering away at a rule, with such a poor understanding of what's actually going on.
You say that cover "in the rules, grants a +2AC." Correct, it does. But then you use this to argue that high ground should give advantage. There is a significant difference between "removing the enemy's +2AC buff from cover" and advantage from height. Advantage:
a) is basically a +5 bonus (2.5x more powerful than +2)
b) weakens the power of other things (spells, feats, class abilities) that grant advantage, since advantage doesn't stack.
Getting a +2 bonus from height would be more reasonable (and in line with your usage of the rules). Heck, I'd even accept getting a +4 bonus. But the fact that it grants Advantage weakens or invalidates so many other aspects of the game.