Still don't see how 2 units of "synthetic" straddle is different from 1 unit of regular put+call straddle, since they would give you the same exposure. The only difference, as newwurldmn points out, is that shorting the stock has a difference treatment from margin and funding perspective.On one side of the long straddle, you don't have theta or any of the greeks to contend with. Every 100 shares of stock is worth 100 deltas. It's a delta neutral set up, with lots of possibilities for adjustments.
Even if your stock fell to $0.00, the delta neutral puts that were purchased at the same time would have you swinging from the chandeliers for joy.