I own an air knife. I love it. I've only had two problems. One is that the jet tip came off in a aeration hole (and I didn't notice it right away - I must have dug up 50 holes looking for it!). It is easier to remove the air knife from a hole if you twist the wand as you pull it up, but I've since learned that it is very important which way you twist when removing it from a hole. If you twist it clockwise, over time the tip will work itself loose, and it's a $250 part.
The other is that the deflector shield gets stuck on the shaft when it gets dirty, and you have to rinse off the dirt in order for it to slide up and down again. If the shield is not against the soil surface, soil is blown everywhere, including in your ears, eyes, nose, mouth, down your shirt, etc.)
As for a compressor, I rent the 185 cfm diesel tow behinds that are always available at any rental yard. I don't use one enough to buy one (they're pretty expensive), plus I don't want to have to maintain it.