^^^ The only significant, consistent benefit of cayenne powder. Yes, the egg color is nice, but nutritionaly, there is essentially no difference. Other results largely arise from small studies whose findings are contradicted by others of similar size.Another benefit of Cayenne pepper is that it can help keep squirrels, chipmunks, and other critters out of your feeder, since they CAN taste the spicy.
One of the largest studies I saw in use of pepper in feeds (actually a capsaicin extract) used 180 chickens - 6 cohorts of 30 birds each, and really talked up the benefits of the red pepper - but the study with feed supplimented by just red pepper wasn't substantially better than the others. The two with red pepper and olive oil are the data points the emphasized, while downplaying the olive oil... and with that, you should have no difficulty finding the study I read.
It was also a very short timeframe, as is regretfully typical.