I've camped there 4 times. Once in June after a late storm. So cold all our water froze. Couldn't eat anything on the top due to altitude, so we got up and bailed fast. Second time at the end of a 4-day hike starting at Onion Valley. Altitude issue wasn't as bad that time.
Another a few years ago with Bob Rockwell, commemorating Norman Clyde's Highest-to-lowest in one day. We camped at the summit, then descended and drove to Badwater that afternoon, with dinner at Furnace Creek. I acclimated for that trip by spending two nights at 10K (Horseshoe Meadows) before climbing Whitney.
Last time was at the end of a Mineral King to Whitney Portal trip. No altitude problems, since I'd been out so many days.
It is perfectly ok to camp on the summit. There are a few flat spots around, one even protected by the surrounding slabs. You will likely be joined by JMT hikers coming up to catch the sunrise at the end of their JMT hike.
The best part of the overnight stay is watching the sunset AND the sunrise. I've slept outside the hut several of those times -- twice without a tent. ...only one of those, a breeze came up and was rattling my trash bag ground cover so bad that I got up and moved into the hut.
To sleep on the summit, you need to start up with at least 3 liters of water -- one for the climb, one for the evening, and one for the trip down. It's probably easiest to eat your biggest meal at the last water location, then just snack at the top. Less food and water required at the top that way.
