[junon]

If an LED fries out, then the current will change across the other ones. If they're all going through a single current limiting resistor, then the current across the other LEDs will change, potentially frying them all out due to overcurrent scenarios. This is the case for many different areas of PCB design.

Further, all LEDs have different responses to current (as LEDs are non-linear components and thus ohm's law doesn't apply) and thus usually require different current limiting resistors to achieve similar brightness or in some cases color.

Also, switching LEDs on an off will affect the cathode net and anything connected to it, so it'd also affect the other LEDs in parallel depending on which are on and off at any given point.