This would seem to be a classic example of a distinction without a difference.

Air tools are far more field serviceable than electrical ones. Furthermore, if your gas engine dies you can fairly quickly rig up something with a horse and a treadmill to spin the compressor.

It has to do with wanting something they can in principal maintain forever without outside help.

Up to a point central compressed air solutions do have H&S issues I recall one of my thermo fluid lecturers saying well if the main pressure vessel failed it would have demolished the building.

They make many pressure rated air hoses in those communities? Didn't think so. As previous poster noted, it is all effectively arbitrary window dressing.

If it where the case they should be using belt drive driven by wind/horse power - until fairly recently mech eng techs in the uk where taught how to design belt drive systems

Belt drives are far more limited and attached tools are not mobile in any way whatsoever. Not even close when it comes to substitution technology.

well machine tools are not that mobile and neither are air powered tools as you normally use those in abuilding that has compressed air on tap.

From my experience with the Amish it is all about justifications that don't make any sense. But if it works for them I'm not going to judge them too harshly.