Well, yes, in "Mudd's women" they were crippled without the crystals. That's a pretty glaring design defect, and I'd expect that after this episode, the ship spent the next couple of months in drydock getting this design defect fixed, so that you didn't need the same "energizer" for all possible power systems.
I'd hardly call it a "design defect" if an aircraft were crippled by losing both wings, or a ship by losing all propellers...
"Mudd's Women" might already describe a pretty robust ship that can go to warp with or without dilithium. It's just that Scotty didn't dedicate time and resources to bringing the backup power system online when Kirk decided to pursue the other option of obtaining more dilithium. The backup need not be "defective" just because it wasn't significantly more robust than the primary in face of exceptional strain.