The only ones that I thought don't touch their sheds whatsoever were B. giganteus and B. discoidalis.
My other Blaberus species (Aside from my fuscas, but I just got those and haven't observed any molting yet) never have old sheds laying around. Parts of them, like legs, yes, but not the whole thing.
Maybe babies nibble on the sheds? It would make sense, seeing as the exoskeletons of the young in most species are noticeably thinner than the adults. (Prime example; G. portentosa.)
One of the things I noticed in my mis-molting discoids was that the front half of the roaches were getting out while the abdomens were stuck it. It looked like their abdominal plates didn't have the split running down them that you'd notice on a molting roach. Also, the whole group looked "thinner" and a lot different than the earlier generations. I kept the diet the same and actually added a lot more fruits than I had before. The humidity was sky-high; I had phorid flies all over in their enclosure.
Any other input on this shed-consumption theory?