I have heard of a few people staying over on the summit out of choice but I don't recall anyone ever wanting to do it again.
This is just my 2 cents though I havent myself camped at the summit but I think you would be hard pressed to even find a flat area big enough to comfortable bivvy let alone set up a tent. The entire top is large rocks that people have to climb over to summit, as you well know. I also didn't think it is considered good form to use the summit hut for casual overnighting. Perhaps someone can chime in on this?
Also I have always read the above 12k ft you aren't supposed to ascend more than 1k ft/day for acclimatization sake. That is probably just heresay anyhow and isn't much a push past considering Whitney is only 14.5k. Probably a better rule for expeditions doing much taller peaks.
It would be a cool idea just if you wanted the experience of being much colder and less comfortable but I don't envision any trip plan that calls for an overnight up there out of necessity.
