I showed the start of an air pruning in "It's in the bag". Those plants both survived and are still going.
They both put out multiple sprouts from the base but not the branches. I pruned the branches off while I could still get to them without endangering the new growth. I put the best of the pruned cuttings in cups and two (out of maybe twelve) did sprout. So, maybe I should have waited longer to prune. Some of the cuttings were off of my one in ground fig, so I'm not sure if the ones that took came from these plants.
The larger plant (on the left) took right off while the one on the right struggled. It put out a shelf fungus from the main stump on the other side from the sprouts and I didn't think it would make it but then it took off too and here's how they look today.
The many sprouts on the big plant were all going straight up and crowding each other. I pruned all but five and tied two to a stick to spread them to the sides, and one to the fence at the front.
They were eager to rise and I had to retie them every couple of days to keep them spreading. I pinched the ends of the other sprouts when they had six leaves to get them to spread so I'm getting a good dense bush there.
I'm seeing very little root coming through the bag and air pruning like I did with the elder roots. I expect that like I saw in my "kiddy pool SIP update" The roots are hitting the bag, turning down, and going out the bottom. I'm afraid to look because those bags are so easy to put a finger through. I wish I had gone to a screen instead of a bag, like Charlie is proposing in "Fig doodle". I would use a finer mesh than half inch just to keep the soil mix in though.
The two issues you have to consider if you're doing it as a raised bed planter is water and cold. You lose water to evaporation off the bag and if you're above ground cold can penetrate deeper. Unless you're raising the bed awful high I don't think you're going to gain much through air pruning. It's going to be dry at the sides and if it's open to the ground the roots are going to run down looking for water rather than becoming dense like you want them to.
When these plants were potted, on the porch for the winter, they were in a blow-away greenhouse and on a heated surface. They still froze back to the ground and if they hadn't been heated I'm sure I would have lost them. If they'd been in a raised bed out in the yard I expect I'd have lost them there too.
It's been in the low nineties and sunny, the plant on the left has been going through a gallon of water a day. When it was in the hundreds last summer I couldn't keep enough water on my potted figs to keep them from wilting. We haven't seen that kind of heat this summer, yet, but I expect the SIP to make a big difference when we do. Maybe a drip system would be enough but I was top watering those pots all they'd take 3-4 times a day and I couldn't keep up. I left these for four days (sunny and in the 90's). I soaked the bags and filled the (3 gal.) reservoir's before I left and the bags and reservoirs were dry when I got back... but the plants hadn't wilted.
I think that if I wanted to go with the Japanese style pruning I'd do it like the Japanese do it and put them in ground then train them to stay low. What I'm doing with this setup is trying to build the best possible root ball before I put them in the ground. I am training them too, and I could train them to that Japanese shape then plant them when they're big enough to be winter hardy.