"Eventually you will also see noise on the LEDs when you have long wires supporting the shifting registers control lines."
If the 7219/7221s are wired up next to each other with the SPI lines wired nice & neat, I don't think that would be a problem.
Each 7219 only turns on up to 6 LEDs at a time in my configuration (2 RGB LEDs per cathode 'row'), it multiplexes them at 800 Hz, flicker free.
So 120mA x 16 '7221s = 1.92A. Not much at all really.
The code could then just update the data that changed, and not have to refresh the whole display every frame cycle.