It would have to be two big batteries. One big battery would only give you 3.6 volts, not 7.2 volts. Then you're back to charging in a serial arrangement and that's actually probably the biggest problem. Two batteries in parallel will be forced to stay in sync with one another, and as long as one isn't vastly worse than the other, probably not a big problem.

The other problem is that in order to maintain the economy of the thing, you want to use commonly used batteries that are made in the hundreds of thousands. 18650s have GOT to be the most common LiIon cell in the world, by a huge margin, because it's the cell used in laptop computer packs and other things. As soon as you switch to a different cell, you're probably going to double your cost right there.