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Has anyone any idea how these bars affect 'crumple zones' that protect the occupants in a side impact or rear impact collision ? And why are they even necessary at all ? Does Toyota Recommend them ?

The Prius currently has a two point brace, which was removed to install this four point brace. Is the four point brace necessary? It's all personal preference. That's similar to asking whether the V actually needs 17s tires... I bought and installed it because I wanted strengthen the chassis, which I felt has a little too much flex due to the sunroof.
As for crumple zones, I believe those zones are designed primarily in the front quarter and rear quarter of the car. The purpose of those zones are to keep the "passenger cabin" relatively intact if subjected to a frontal or rear collision. Since this brace fits within the "passenger cabin" of the car, I don't see how that would affect the crumple zones.

I'd have to agree with HI MPG on that. To directly answer the question, NO. They're not necessary. If you were going to install something like this, you're limited to two options. A BT tech type chassis plate which doesn't seem like it would make a difference at all, although everyone owning one seems to praise it. In structural "racking" where one side moves the opposite direction of the otherside (in this case I'm talking about the factory chassis brace being inadequate) the brace bolts would have to be moved further apart from eachother in order for this device to work. Comparing all the other chassis stiffening braces on the market, this one doesnt utilize the factory holes and seems to make the most sense. I also agree with the "crumple zones" theory. The reason people install these braces is allegedly to stabilize the vehicle in high winds at highway speeds, and also wind created by larger vehicles namely semi's while driving on the highway. I have not installed either at this point, but have been researching the snot out of all chassis stiffening products on the market because I just dont understand how they could improve anything. This one however, makes more sense than all the rest and I just saw it for the first time.

Did you contact Toyota and get an OK before installing them ? I would be concerned about the consequences in a collision, and your insurance company claiming they can't accept responsibility of damage due to a non Factory approved modification of the cars structural design. They might even go so far as to claim they affected the cars behavior, and contributed to the crash.

Uh... I wasn't aware that I needed Toyota's permission in order to modify my car. By the same token, did you contact Toyota to ask for their OK to pinstripe your car with reflective tape? I could see other drivers arguing that they were distracted by the reflective tape...
If my insurance company were to claim that the parts caused the accident or damages resulting from it, I would ask them to prove/replicate their claim.

I was told by an Illinois State Police officer that you cannot have white reflective tape on the back of the car, that color of reflectivity is reserved for emergency response vehicles.