Why can't resistors be used to connect cathode pins to GND instead of segment pins to VDD with a 7-segment display?
The purpose of the resistor is to limit current to a segment LED, by dropping the surplus voltage (over the LED Vf) across itself.

When a resistor is used on a common cathode, the current through this resistor would vary by the number of segments lit at any time. Thus, the voltage dropped would change as well.  This will lead to intensity of digits changing with number of lit segments.