Good points all around. It looks like the forward voltage requirement for the white LED's is about 3.5 to 4 volts so I guess a doubler isn't really necessary although some sort of boost would be. And yes, it would be silly to boost a single cell to 2x the voltage and then regulate it down to whatever. However, a manufacturer could certainly build the required boost circuitry into the regulator but no one has. I'm just wondering why not.
The whole 2S concept just seems like a poor design to me. Maybe I'm over-reacting since there are obviously a large number packs out there operating with what appears to be an acceptable failure rate but it shouldn't be that hard to eliminate the need for 2S packs. Another option would be to incorporate balancing circuitry into the pack, maybe as part of the protection PCBA. I can understand why a mfg like MagicShine might skip this since they seem to be very price sensitive but it is surprising to me that no higher end mfg's have pursued this.