When you trade your old game you loose the privilege of playing it because you need the disc in the drive. It makes perfect sense to invalidade the first install as soon as the second is activated if not, before it is even purchased by someone else.
Actually it makes perfect sense that if you bought the game on a disk the install would be rendered useless as soon as someone elses buy that used disk and installs it. Currently when you sell a game you loose the options to play it again because you need the physical disk. This way the fee charged by microsoft would cover a part of the loss. There is a lot more to the price of game than what microsoft charges the user (retail, packaging, fees to studios etc etc)