I'd be interested in an experiment to gauge total wort recovered by just letting the bag drain for 30 minutes vs squeezing like a mad man.
I have a hunch there is not much gained if any squeezing vs a patient drain of say 30 minutes.
I actually tested this and the answer is "it depends on the bag and the grain bill"
Your bags are by FAR the best gravity drainers and 30 minutes resulted in about 2 cups difference in finished wort volume.
The brew bag after 30 minutes was nearly 0.75 gallons short and required squeezing to get the rest. I suspect the two nylon straps inhibit drainage.
A paint strainer bag was about halfway in between.
I also found that the "squeezed wort" seemed to have a higher concentration of sugars than gravity drained wort. I didn't test this for repeatability though. My theory for this is that, like a sponge holding salt after a saltwater dip, grain will always retain some sugars under the weight of gravity. So squeezing liberates water faster and more sugar stays in solution due to the higher volume of water coming out.
The efficiency difference was about 6% on my system.
So I do attribute a small lautering efficiency increase to squeezing, I'll usually do a combination of hanging for about 20 minutes then squeezing the rest out.
Grain bills with oats or flaked adjuncts retain water like crazy and really do need to be squeezed.
The old astringency issue is a non issue. It just doesn't happen. Astringency is the result of a high ph coming into contact with the grain husks, or heating them too much and extracting tannins. Tannins are a water soluble compound under specific conditions (pH and temperature), and are otherwise not soluble.
Saying "squeezing can extract tannins" is the same thing as saying "I can dissolve a bone in my soup if I stir it hard enough"
Sure bone will dissolve but you have to boil it long enough in the correct chemical conditions.
I've squeezed nearly every batch I've ever made in a bag, more than 100, and I've never once experience astringency.