There are a couple of big problems with the conventional analog joystick system. First of all, the crude analog-to-digital conversion process isn't very accurate, since the system doesn't have a true analog-to-digital converter. This compromises the joystick's sensitivity somewhat.
Second, the host computer has to dedicate a lot of processing power to regularly "poll" the joystick system to determine the position of the stick. This takes a lot of power away from other operations.
Next, let's take a look at how designers have addressed these problems to date.