White whales are kept at several U.S. aquariums (including the one in Chicago), as are their close cousins the pilot whales. But those are small cetaceans, much smaller than killer whales. Whale sharks fill out to exceed 35 feet in length, which would require a massive aquarium indeed. A baby whale shark starts off the size of a dolphin!
Public aquariums spend small fortunes DAILY on food for their specimens, just like zoos. I've taken care of dolphins before... a couple buckets of fish daily, plus vitamins. It ain't cheap. I'm sure most if not all of the money made off the limited diving ops with the whale sharks goes straight into upkeep costs for the animals.
"Look and don't touch" isn't a hard rule. It's primarily in place for uneducated or unsupervised divers, and then mostly limited to sensitive habitats. If you've seen diver ops in places like DisneyWorld or many public aquariums, they're usually tightly regulated by staff divers, or the volunteer divers have been through extensive training. Captive animals also develop greater tolerances to human interaction than wild ones... this can often backfire when the critters have to be released back into the wild. Sea otters and dolphins are particularly problematic in this regard, and require extensive "rehab" before they can be released back. It often doesn't work, anyway.
Fortunately whale sharks are rather er... stupid.