Richard Holliss and Brian Sibley's The Disney Studio Story was one of the few pre-1996 sources I have been able to find that discussed the subject with any substance. They said:
I watched the short version many, many times as a child. But even then I got the sense I was watching the edited for TV version of a much better film. I only made it through the even shorter TV edit once. On my 14th birthday, when I received the 25th anniversary laserdisc as a present, I got the greatest gift of all: I was proven right. Things that were unclear in the theatrical cut were clarified, and the sloppy jump cuts in the score were gone, and I finally realized that "what effect a little smoke is with a dash of hocus pocus and the scent of burning sulphur in the air" was actually part of a song that wittily explained the difference between fantasy and reality.The way to please all fans of the film—a choice between the version the studio wanted you to see and the film the creators actually made—was in Disney's grasp, but they let it slip through their gloved fingers for no good reason at all.In an attempt to stop Bedknobs and Broomsticks reaching the tedious length of its disastrous predecessor, The Happiest Millionaire, the picture was ruthlessly edited — so much so that Roddy McDowall's performance, as an unctuous curate after Miss Lansbury's hand, was largely left on the cutting-room floor. Also lost were several key songs and most of the characters' motivation. It is perhaps surprising, therefore, that what remained was as good as it was.Reviews of what the Disney publicity men called a 'bewitching, bedazzling, magical musical!', were mixed; Films Illustrated dismissed it as 'a computer-built entertainment designed to pick up where ... wisely left off.' Others, like John Russell Taylor in The Times went so far as to say that 'the same as before is better than before'. One critic hazarded that Bedknobs and Broomsticks would 'take a mint of money'. On its initial release, it in fact took $17,500,000, a respectable sum had the film not cost almost $20 million.