The prohibition against alcohol came directly from Walt Disney before
Disneyland first opened in 1955. Walt wanted his new park to a family place; he didnt think alcohol fit that image. The amusement parks at the time often sold beer and had reputation for being crowded with drunks. Disneyland was supposed to be completely differnt from the typical amusement park, the ban on beer was one more of those ways. And this was the 1950s, there was much wider distinction between what was acceptable private behavior and what was acceptable public behavior.
Walt himself had no problem with adults drinking. His own afternoon scotch became legend around the studio lot. And there are numerous stories about the party thrown in the Golden Horseshoe Saloon the night before Disneyland opened (including the one where Walt was so drunk he had to be carried to his Main Street apartment).
When the Magic Kingdom opened in 1971, the no alcohol policy was such a popular part of Disney tradition that it was continued. The MK was to be a family place too. However, the rest of the resort was more typical vacation destination and all the resorts opened with full bars and restaurants that served wine and beer. Even the shops in the hotels carried those little airline sized bottles of booze. But that was adult stuff that was kept away from the kids and out of the Magic Kingdom.
The policy was changed at Epcot because the park was designed mostly for adults, not children. And alcohol is a significant part of many of the cuisines offered in the World Showcase restaurants. A French meal is impossible without wine (an issue that would reappear with Euro Disney). In the Eisner era things became so much simpler. The profit margins on any kind of alcohol are huge and it was mandated from early on that the Disney/MGM Studios would serve as much as possible. The Studios was also the first theme park to open with two full fledged bars the Catwalk Bar and the one the one adjacent to the Prime Time Café.
Today alcohol represents a significant profit center for WDW from the parks to the ancillary gates to the golf course (those drink carts make a ton of money) to Pleasure Island to catered events at the resorts. There are almost annual proposals to change the MK no booze policies and there has been the occasional special event that sold alcohol. Most people now consider it only a matter of time before the beer wagons show up on Main Street.