It might be possible to get a healthier BP by feeding it a varied diet.

However... as has been pointed out, there are no studies to either prove or disprove this.

We do know that BPs can live long, healthy lives when feed exclusively rats and/or mice. It appears that they get everything they need in balanced ratios from this diet.

We do know that BPs can be prone to hunger strikes. One of the things that has been observed to throw them off food is offering them something other than their usual.

Compare this with your example of an iguana, where we know it does not get everything it needs from any one food source. And, although I don't know much about iguanas, I'm not aware of them refusing to eat Veggie A anymore after they are offered Veggie B one time. So iguanas get a clear benefit, and not much risk from a varied diet. A BP gets no known benefit, and a known risk from trying to vary their diet.