I'm not a fucking scientist don't get me wrong. We're just talking hypotheticals right.
Mate, there are two things I've learned about growing.
1. If it works, it works
2. Reliability trumps performance
All the theory in the universe doesn't beat real-world results.
Likewise, you can have the most efficient system in the world, but if it is prone to blockage or breakage - blocked lines, pump and timer failures etc - then the loss of an entire crop puts you right back to square one.
Good growing is really a balance between performance and reliability - just like motor racing or just about any other sport.
Maybe you can try both set-ups on a flood table to see what the results are. That's the only real way to determine if cloth or air pots have a real-world advantage over sealed pots in a run-to-waste system.
My initial thinking is that with a sealed pot system, every time you water it, the soaking action pulls air down with it into the root zone. The air and nutrient solution can only go in one direction - sucked in from the top and expelled out the bottom. This ensures delivery to the entire root zone without any bypass.
It also ensures proper flushing of excess salts.
With an air pot, there might be the possibility of nutrient solution going in the top and not making it all the way to the bottom of the pot, as water takes the path of least resistance. If the pot is root-bound, and water can leak out the sides, it just might follow that path. Or, you may have to use a little extra nutrient solution to ensure the entire pot gets a soaking. I can certainly see where the extra evaporation and leakage would cause you to use a lot more water, so you might have to refill your reservoir more often.
I'm certain air/cloth pots would work, but how much better growth would you get? I don't really know.
I do know what has worked for me over the years, but that doesn't mean your proposal isn't a better one. If it works, it works.
Just make sure it's reliable!