The don't work "without mirroring" because then you are not mapping the second ROM to the right location. There is a good chance the actual mirrored data isn't accessed at the mirrored location. It might be, but alot of the time mirroring is not required.
If you want to try it out, take one of these games you are mirroring by copying the ROM. Instead of copying the ROM to fill in the "mirrored" part, just copy blank data of the appropriate size to fit before the second chunk of ROM. I'd try but I don't have a flash card handy.