Stats on car accident injury rate vs BMI would be interesting but I'd imagine something like "the fatter the safer" (up to some level) would be the conclusion and so testing on skinnier model is harsher and will result in better safety.
It shouldn't be hard to spec and built crash test dummies with simulated fat.
Some possible downsides would be overwhelming the airbags capacity, and larger overall volume of space which needs to be protected from intrusion/crushing/etc. I Wonder how much this has been studied, hard rubber and steel dummies probably don't reflect conditions at the extremes very well...
That is in part also why it is so important to have a properly tightened seat belt and why we have explosives to tighten it up further when a collision is detected.