As a compromise, instead of removing Height Advantage altogether, they implement a Height+Crouch feature. So, basically, if you are more than 10 feet above your enemies, and you Crouch, you force all enemies to get a Disadvantage on all rolls against you because you are on higher ground and getting lower to the ground. Thus, you reduce your own target surface area, making it harder for an enemy to hit.
You still wouldn't get advantage on your ability to hit lower targets, but it would be harder for them to hit you.
In 5e you can voluntarily go prone to do this, (think like dropping in a sniper position). There's also the dodge action, but dropping prone can be done as a free action and only costs half your movement to get back up.
I'm 100% for having free-action prone in game, dodge action in game, and disadvantage from low ground removed. It would be a dream and make combat have rich depth. Prone could be added next to the bonus actions and dodge could go with the actions.