It's not quite as simple as Walt wanted it to be dry.
You need to look at the history of the parks, and what made Walt Disney innovative.
Before Disney Land, you didn't have modern theme parks. You had carnivals, that had some rides.... and were typically staffed by unsavory characters. Alcohol was rampant. people carrying around their beer as they boarded a ferris wheel.
Walt Disney's innovation was to take those classic carnival rides, and create a park where families and young children felt totally safe. Where going to the carnival was an expression of youthful innocence.
And thus, you say some elements that completely set the Disney Parks (Disney Land and the plan for Disney World) apart --- The parks should be exceptionally clean. Workers were had to be clean shaven --- Facial hair was not allowed. And the park was dry. These types of elements, made people think of a Disney park as being completely different than the other carnivals they had seen
The Disney model was so successful, that you had many copy cats. Theme parks were born, as elaborate modern carnivals, that were geared to clean fun for families.
So as Disney built additional parks, various rules came to be relaxed. People already think of Disney as being "wholesome" --- People think of theme parks as being "wholesome"... so there is no longer a need to take extra steps to prove that wholesome image. And of course, alcohol is highly profitable. So they built additional parks, and looked to incorporate alcohol in wholesome ways -- How could you really have a World Showcase in Epcot with Saki in Japan, beer in Germany, and fine wine in France?
How could you truly claim to present fine dining, without a wine and cocktail list?
Today, Magic Kingdom remains "dry" out of the tradition and legacy, though it is really no longer necessary. If Disney restaurants began to offer alcohol, the only outrage would be a couple threads on message boards claiming that Walt was rolling over in his grave. (With the current state of theme parks in our culture, I don't personally think he would care). Most people wouldn't even realize that there was a change.
Similarly, in recent years, Disney relaxed its rule about no facial hair for cast members.
So Walt didn't oppose alcohol in the parks as a simply because he wanted it to be child friendly, or anything like that. It was a tactical decision, to create a brand very different from the carnivals that had existed up to that time. His creation of the private club at Disney Land demonstrated he wasn't averse to selling alcohol.