I believe webbing should be applied using large ( 5/8″long) upholstery tacks, not staples, so that the webbing will be secured firmly to the frame. Upholstery staples, even those applied with a pneumatic stapler will not be strong enough to hold the webbing. A webbing stretcher is essential to making the webbing tight enough. The webbing also holds the wood frame together tighter and the seat is more resilient than one made with a plywood base.
I have taken apart quite a bit of upholstered furniture and it is quite safe to say that upholstery tacks haven’t been widely used in manufacturing for decades. Upholstery tacks were once the standard, but they have been replaced by staples. Both the jute webbing and the modern polypropylene webbing can be installed with staples. The polyprop webbing in typically green and black and very elastic. A large portion of European furniture is made with this webbing which is applied with staples. Someone with ample arm strength could apply this stretch webbing without a stretcher, however, when applying the jute webbing a stretcher should be used.
As for webbing versus plywood, for the most part these applications are not interchangeable on the same piece of furniture. It can be very surprising to discover just how little thought has gone into some frames. (mainly the older pieces)
Today the focus is on lean manufacturing and saving money. I once had planned to use nailhead trim on the back of chair- but found that i couldn’t because there were gaps in the frame! Some chairs are designed for plywood bases, and under no circumstance can you change that. One clue is whether or not you actually have a stapling surface.
The B and A after pic, this chair does not have a stapling surface. Its wood trim is finished for show, thus the use of a plywood insert. is the only option.
The above sample does have a tack / stapling surface. In the days of old not only was the webbing tacked, the fabric was too. However, as old as this chair is (the fabric was applied with tacks) it did not employ webbing as a foundation. And to prove that you can see alot of strange things, I recovered a pair of these chairs and the framing in the seat area was done two different ways.
In upholstery you will see all kinds of things and your decisions will always be tailor made to the specific details you are working with.
Please write back with any feedback.