Well, the endgame is not the hardest phase of the game, but the one where you actually have to play chess.
For example, I know several people who can calculate middlegame combinations, but get lost in an endgame. Reason? Mostly they don't grasp what are they supposed to be calculating, or get into a worse position firmly believing they're doing good.
Openings and middlegames do require calculation because the methods for evaluation are not precise enough, but somehow the majority believe they can do it safely by following recipes and general rules. As their opponents usually do the same, they don't get punished as often as they should (I mean, to stop "playing" that way).
A century ago Capablanca told everybody –new to the game– to begin by studying endgames. Some thought it was memorizing... and as that's boring few took the advice. Endgames are about making a few pieces to work as a single unit following an idea, are about threats to keep the rival from achieving the same. Endgames are about doing the previous idea with the least amount of moves. And in the end, are about promoting a pawn and checkmate.
I am doing endgame lessons and it is striking how much precision and calculation is required to play it right. Kings and pawns are all short range pieces, which require a lot of calculation to find out if a particular move is good or not. And it is not uncommon that a specific move wins and ALL other moves either loses or draws. In other phases, there are usually several decent moves and mistakes are easier to repair.
Also, when i play opening and middle game, i can use a lot of intuition. I just know from experience and strategical understanding that a specific square is good to develop a piece to. I don't need to calculate that much, other than the forcing moves. There are times where i can use intuition during endgames too, but more often than not, its about calculating to make sure i have the opposition after tons of king & pawn moves/trades, or if i will have the time to promote a pawn or not after a series of king and pawn moves/trades.