With Super GT cars the handling improves a lot almost second a lap on some tracks. So you cant go wrong.
With street cars I dunno, havent tested yet.
I've done testing of this and I can say this isn't true for me. The lap times are nearly identical and consistent.
I ran three tests using the WOODONE GT-R at the 10 lap A-Spec Suzuka Super GT race in perfect conditions.
I purchased three WOODONE's from the NCD, washed them and changed the oil.
The HP was 503 and PP was 597 after setting the Aero to MAX. No other changes were made (used stock suspension and LSD settings).
For the first one I added the Chassis Reinforcement and ran the race. I threw out the first lap and then threw out the best and worst lap times. A total of 7 lap times were collected.
For the second car, I did
not add the Chassis Reinforcement and repeated the race. I threw out the first lap and then threw out the best and worst lap times.
For the third car I added the Chassis Reinforcement and did the same thing.
The lap times for the first test were 2 seconds higher on average than the 2nd and 3rd tests. This was because I was learning to drive the car/track.
But the 2nd and 3rd test were very, very close and I think, given my new-found experience with Suzuka and the WOODONE, I could get a touch faster every time I did the test, regardless of the Chassis Reinforcement.
Logically, the Chassis Reinforcement (or Body Rigidity Improvement as it is called in the game manual) shouldn't be needed on race cars unless you increase the HP or lighten the weight. Racers should already have their own reinforcement.
As for street cars, they "need" the Chassis Reinforcement most of the time. As they were sold, they weren't meant for racing. The exceptions could be cars like the Ferrari Enzo, which is made to be extremely fast, but I think if you increase the HP or lighten it, it would "need" it as well.
I put need in quotes because individual results may vary. I am only speaking in terms of real-world logic relative to turning a street car into a track car.