I tried exactly what you are suggesting many years ago when my parents owned an Oreck XL. Back then they had 4 layer dust bags and the original 2 layer green dust bags for the Oreck. It kind of worked - but the problem was that once you cut a bag in half, or however you do it, you'll loosen the sealed paper to the bag, causing the layers to fall in, making it difficult to tie the bag around the round dust channel feeder in the bottom or top fill tubes in the Hoover uprights. I found that, compared to the 300 watts of the Oreck XL, the increased power in the Hoover uprights often pulled the bag away from the rubber ring, no matter how many times i tried to get more of the paper's top over the ring. Clearly although Hoover's own bags had dual layers of filtration, they were designed to fit instead of using another brand's dust bag.
I've often wondered why it wasn't possible for brands to offer a zipped section of material similar to an electrostatic filtration that could be attached to the inner part of the outer soft bag of an upright vacuum. That way, it could hold back any escaping dust as well as act as a main filter and allow owners to just take off the inner section of material after the bag instead of have the owner remove the entire outer bag for periodic cleaning. Hoover evidently just didn't bother to offer this and instead had the owner go through the palaver of removing the entire outer bag should it get caked in dust - brushing it out could only remove it half way, damp cloth washing the inner bag often meant ground in dirt often got more ground in unless you were lucky enough to own another vacuum, like a cylinder vac to suck out excess dust that had clogged the outer bag that had come from the dust bag.