Because Walt died before the other parks were built.
Seriously, that's the short answer. He was often quoted as saying that he felt that the presence of drunks ruined most "carnival" experiences for families, and that was the reason why he wanted his theme parks dry. (He was NOT a teetotaler by any means, nor did he feel anyone else should be, he just thought that drinking tended to get out of hand at "amusement" parks and that he didn't want that marring the experience at his.)
Had he lived to see the construction of the other parks he almost surely would have insisted on keeping alcohol severely restricted there as well.
The middle paragraph is true. He was building a brand, he was re-defining "amusement parks." Why would people trek across the country to Anaheim or swamp land in Florida if they had local amusement parks? Because the local amusement parks were seedy affairs. So these redefined parks... the point was to make them as clean-cut as possible. To distinguish them from the carnivals of the time. This was strictly a business decision, a marketing decision.
By the 1980s, when Epcot was opening, the American view of an Amusement Park had changed. Walt had no objection to serving alcohol -- even Disney Land has/had a club where alcohol was served. Customers no longer needed to be sold that Disney Parks were family friendly. People trusted that Disney Parks were family friendly, even if the French restaurant in Epcot served French wine!
And Walt Disney --- His greatest consistent motive, was profit. He was a pure American capitalist. Alcohol is highly profitable. Thus, if he could now make profits from alcohol, all while preserving the family friendly image of Disney parks? He'd be all over it!