Great whites are one species I'd prefer to see from inside a cage. I've gone on 'shark feed' dives to see tiger sharks (none over 10 feet long; they can hit 16!). The question has come up on the forum in the past...would you knowingly get in the water with a great white (no cage). Some years back one of our more seasoned members related an account where this situation came up (I think it may've been at an oil rig?), and while the Captain seemed to think it was fine to do (I think as in 'You're here, pool's open, go in or not, no refund')...the diver decided not to do it.
It's interesting we don't see a great white equivalent of Tiger Beach in the Bahamas, where people go to dive cageless with tiger sharks. I've read of one guy who took people out in South Africa for cageless encounters.
There's a video on You Tube somewhere with a guy in a 'ghost box' (transparent acrylic box about the size of a small coffin...how appropriate) in water with good viz. with plenty of great whites around. One eventually gnawed on that box (with him in it).