The terrain already provides terrain-related benefits. It's also why D&D has speeds for climbing and rough terrain, to capture the benefit of terrain.

Advantage is a specific term for the game, literally Max(2d20). Disadvantage is a specific term for the game, literally Min(2d20). Advantage is not a composite for real life terrain advantages.

Having terrain benefits and a swing of AdvantageFOR/DisadvantageAgainst is overkill.