Now, now. Let's get our logic straight. If the first collision does not happen, there is no secondary collision. Besides, body dynamics is so complex that they still use crash test dummies, not simplistic commentary. For example, in a HARD rear-ender (none of this matters in a fender bender), without the hoop, your head might snap back and sever your spine; but the hoop might stop that, and then cause a crush injury on your brain. It's all "maybe".
The real issue is that these "street" roll bars are ONLY cosmetic -they offer little safety. Not braced well enough in any direction, tubing too thin and too soft, mounting to the car way too weak. Most important, the hoop is not high enough to protect the head in anything like a roll over, even if it did not collapse. Better tubing, better mounting and bracing, better engineering, and you get a sanctioned SAFETY roll system (and no way to put the top up!). Oh, you also get a $1000++ bill.
If you like the double hoop, here's one that was on the BB a few years ago (thanks to the originator!). The one in the car appears to have a diagonal rear tube (I can't bring myself to call it a "brace"), but it can't go anywhere that helps as the folded canvas top is in the way.
Roebrt