Dont know that hairnets have true drawstrings. Most I have seen just have an elastic type of "seal" which would not keep insects out thst well. I would also question ultimate strength snd durability in the elements.
There is s reason organza bags have been used worldwide. The cist is not that much greater and you knowvwhat you are getting and dealing with.
Yes, organza bags would work with stone fruits (peaches, plums, spples, etc.).