I'd say most of those films were written and produced by Bill Walsh.
Bill Walsh started at Disney in the 40's in publicity and somehow managed to write the Mickey Mouse Comic strip. He soon became a favorite of Walts' and ended up producing some of the early one shot Christmas TV shows in the 50's.
He eventually became the producer of The Disneyland TV series producing one hour of content each week. With Walt impressed by Walsh's abilities, he quickly moved him into overseeing the Mickey Mouse Club producing over 5 hours of content every week!
In the late 50's, Walt moved Bill into the position of motion picture writer and associate producer with The Shaggy Dog. His rise was fast afterwards and soon became one of Walt Disney's top producers. When Walt Disney died in December of 1966, Bill Walsh was considered for Walt's job. He preferred to work on individual projects and turned it down.
You don't hear much of Bill Walsh anymore, but he was considered one of the most successful producers in Hollywood and just about every studio in town made him offers to leave Disney. Bill turned them all down and stayed at Disney right up until his death in 1975. His films were box office bonanzas, movies like The Shaggy Dog, The Absent Minded Professor, That Darn Cat, The Love Bug and Bedknobs & Broomsticks and of course Mary Poppins. As a matter of fact, Poppins and The Love Bug were the top grossing pictures in their years of release!
Walsh would often work with Disney story sketch man Don DaGradi and create these marvelous movies that were half live action comedy, half cartoon, but somehow in his way of writing these films, Bill Walsh was able to take things that were far out in conception and make them plausible. If you remember Basketball Players bouncing up and down on a court, or a Volkswagon skipping like a stone across water, or people have tea parties on the ceiling, then you're remembering something dreamed up by the imagination of Bill Walsh and Don DaGradi.
Walsh's favorite director was Robert Stevenson because of his detail oriented, no nonsense approach to movie making. Because Walsh used storyboards to pre-direct and nail down every element, Stevenson adhered to them and focused on accuracy and performance. When all the cylinders were working, the results were often magical.
Out of all the executives at Disney, Bill Walsh had the respect of the creatives. He was as close in spirit to Walt Disney as you could get. After Bill Walsh passed away, many animators in the studio considered retirement because Walsh was one of the FEW creatives left in management. Bill was so devoted to Walt Disney and the studio in general, that when he died, Walsh was buried within a few feet of Walts' final resting place in Forest Lawn Glendale.