We have enough 'supression' in this country as it is. Mostly political in nature...
Additionally, a suppressor on a PCP air rifle isn't regulated by the BATFE at all. In fact there are no regs for air rifles. Like flamethrowers.I can see the day coming when propellant initiated bullets won't exist anymore nor will the devices to fire them either.. Why my next purchase will be a PCP air rifle in the 30 caliber range. Very quiet, extremely lethal. Of course the 'accessories' are expensive, like scuba tanks and or a compressor capable of developing the pressure needed to charge one. but, once you have the necessary hardware, it's all good and there are no license requirements either.
I think taking large game with an air rifle would be a hoot.