There must be a reason for the 120 support material to be different, else it would be the same and you'd be able to cut both sizes from the same master roll.
It's not 120 that's different, it's 35mm, originally we had sheet film, which was quite thick because it needed to be stiff. Then when they developed roll film, they made it very thin so it could be easily wound on the spools. 35mm had to be thick enough that the perforations didn't pull through, but thin enough that it could still be spooled, so we ended up with three different thicknesses. However a lot has been done to soft plastics technology in the last 100 years since 35mm film stock was developed for motion picture use, It's possible to use a different backing material like polyester which could be thinner but still resist tearing, which would allow you to use a thinner base material for both 35mm and 120 coating.
Really I think it comes down to demand, if enough people ask for it, Kodak will run off a batch, if that batch sells well within the expiry time, they will make another batch. The problem isn't developing the film, heck Kodak has experienced people to do the engineering to do this, probably take almost no cost. The problem is packaging, you need to design a backing paper and a foil pouch a unique box, and the fancy closing tape.
Here is my suggestion for Mssrs Kodak, adopt the use of ink jetting for printing generic backing paper and foil pouches. Ink jetting is the technology that prints the name and address on mailed out printed catalogues and magazines these days, it could be used to simply print the film type, speed and size on the ends of the backing paper, and the sides of foil pouches. Or print all the information and fancy logos and stuff on the foil pouch and eliminate the box.
By the same token, how come they still ship plastic cans with 35mm film, simply put the cartridge in a similar foil pouch and eliminate the box. market the heck out of it to customers less packaging for the more environmentally friendly film user. Also means that the box shipped to dealers would be smaller and the weight would be less.