What's interesting is that Disney - the parks operations part of it - is mainly a hotelier/food service company. Think of it: the huge profits are made renting hotel rooms and selling food, beverages, and merchandise. I would bet the parks themselves (the money from ticket sales) are at best break even, maybe even operate at a loss. The costs of all the CMs, the transportation system, the ongoing maintenance of the attractions, security, all the overhead costs, have to be huge. So they have to make their profit elsewhere.
That said, if they start increasing use of part timers instead of paying a higher minimum wage to a stable full time work force, look out. They will end up with a generally disloyal, disinterested staff that is in constant churn, with constant turnover and training always ongoing. This will impact the user experience everywhere, and they will lose some of that magic they try so hard to generate.
Here in PA the company that runs the service plazas along the PA turnpike pays somewhat above the state minimum wage, which currently is $7.25 an hour. They constantly advertise in the local papers for help, and are constantly training people - who then leave for better jobs once they find one, which isn't too hard when you make so little. And it shows; many of the employees look totally disinterested, have no motivation to go above and beyond, and seem like they can't wait until the end of their shift. That hurts customer service, but since they have basically a captive audience (you have to exit the turnpike for other choices, and the plazas are very convenient) they continue to operate in this manner - because they can.
Unlike the unfortunate customers of the PA plazas, Disney customers have other choices. Right now they still are choosing Disney, but decrease the customer experience on a regular basis across the board with part timers (CMs, hotel staff, food workers, store clerks) and it eventually has to hurt them. That's why I always believed you take care of your employees - those are the most valuable asset any company has.