I believe that shrinkage is the main benefit. If you use a PVA glue the sinew still shrinks, but the glue does not. That means some of the sinews potential is used up pulling on the glue. With hide glue it is pulling the bow into reflex along with the sinew. That, coupled with the sinews ability to stretch without breaking is the “secret” so far as I am concerned.
If you reverse brace a bow, you are compressing the wood on the back of the bow, shortening the back. Then you glue your backing on to this shortened back. Then when you remove the string that was bracing it, the wood tries to return to its original position, tries to lengthen the back. But the new backing stops it from going far, reflex is held. The backing (sinew and glue alike) gets tensioned by the wood trying to return, no shrinkage necessary. If, while drying, the sinew does shrink without the glue, the only potential that gets "used up" is potential to pull the bow in to reflex. Which you don't need because you've done it with muscles and a string. As long as everything adheres and dries properly, the end result seems very similar to getting reflex by shrinkage. In both, you end up with a backing that in some sense is too short for the bow. If do this with both methods on clone bows and you make the amount of held reflex identical, then the amount of pre-tension on the back must be identical. You can tell because it's pulling the wood in the same way.
I'm genuinely curious, did the people you know who tried it with PVA manually induce the same amount of reflex that hide glue would've pulled the bow in to?
If there is a performance difference even with the same amount of reflex, I feel like the difference that my test here highlights is probably the real consequential difference between glues.
