I become frustrated with players frequently, but I only get angry in rare circumstances. One of those circumstances is when a player voluntarily trades his last piece to reach a lost king and pawn ending. Consider the following position that arose in the MSL Tournament:
White is dead lost here. There are pawns on both sides of the board and Black has a healthy extra pawn. Since he can obtain a passed pawn any time he wants by ...a6 and ...b5, White has to keep his king on that side of the board to defend. That leaves the Black king free to run over to the other side of the Board and pick off White's g-pawn and h-pawn. If Black's extra pawn was doubled or backward, White might have a chance, but Black's extra pawn is healthy so the position is hopeless for White. If all the pawns were on one side of the board, White might be able to trade down to a drawn king and pawn verses king ending, but with pawns on both sides, that's not going to happen.
With a couple of rooks on the board, White chances are much improved.
Here is another dead drawn position from the MSL Tournament:
About the best that Black can hope for is to reach a position like the following:
So the position in Figure 3 should be drawn and the players in fact agreed to a draw after a couple more moves. Those moves were 1. Re1 Kd5 2. Rf1 Kd4 3. Rf2 Rd1+ 4.Rf1 Rxf1+ 5. Kxf1 Ke3 6. Kg2 1/2-1/2. Although the players agreed to a draw and the material is even, White is now dead lost.
It is never a good idea to trade off your last piece if the resulting king and pawn ending is a loser. You almost always have better chances of making a comeback with pieces on the board, even if those chances are only marginally better. With rooks, however, the chances are often dramatically better with Rooks. If you add a pair of knights to the position in Fig. 5, White's hopes would improve, but Black still would have excellent winning chances. However, if you add a pair of rooks, Black's hopes evaporate and the position is dead drawn.
Here's the lesson to remember: If your only reasonable hope is a draw, unless you can clearly see how you will get it in the king and pawn ending, keep the rooks on the board.