They definitely don’t continuously use 1200mA under normal conditions. I think when the units start up (with all the lights) it quickly flashes a few watts of power to flash LEDs/bypass settings, etc. But draw under load is significantly less.

An example is the whammy reissue pedals. The whammy I have here says 1300mA but its running off the standard BOSS 500mA PSA supply. Using the cheap, larger 1300mAh supply that comes with the pedal actually sounds worse due to high frequency “whine” (The BOSS PSA is quieter on this particular pedal).
9V*1.3A=11.7 Watts
Checking the actual case with meter:
= 2.7 Watts
2.7/11.7
SO… under normal conditions the whammy runs around 1/4 of its marked power rating.
As far as I know ALL Factor pedals and H9 run off 4.5 Watts (~500mA) supply, 9-12VDC