What reasons are there to rewire an ungrounded circuit instead of adding GFCI protection?
Points one and two, I can't make a definitive answer but generally when a ground is not provided a GFCI provides acceptable protection.

As for point 3, grounding issues are a major source of noise/static.  If the item is not grounded the metal case around the device will be very ineffective in shielding the device from EM interference.  Likewise, any EM interference the device creates will be poorly contained within the case.

Another source of grounding on audio/video equipment is referred to as "ground loops".  Pretty much all audio/video cables use a grounded jacket around a central wire to shield it from EM interference and this jacket also connects different pieces of equipment together on the ground.  If two pieces of equipment happen to be grounded to two different sources, a small electrical current can be transmitted across the grounding jackets causing a lot of noise on the lines.