What if the piece you are framing IS cardboard?
(Yes, I did this - it was a cut refridgerator box a kid had painted with whiteout and black sharpie - his grandmother had it framed for him! You can't tell me that warrants "conservation" framing.)
This reminds me of when I've framed art painted on Mexican
bark paper. It seems a bit silly to be using rag mats on something
that's painted on a substrate far more acidic than a regular
paper mat would be.
When I first learned to frame, we backed with cardboard,
but when the owners of that shop sold it and I had the choice,
I stopped buying cardboard. Since then, I back with either
regular foam core or artcare, and if an extra piece is needed
to fill, I make sure to charge for it. As was mentioned earlier,
you don't need to use two solid sheets extra on deeper
frames. I use one solid sheet , attaching strips of foam core
to get it to the depth I want, and then face the strips to the
foam backing that's behind the artwork.