The film was originally going to be a straight adaptation of the story of Baba Yaga, which Gary Goldman was a huge fan of. He admitted to only agreeing to this so that she could be shoehorned into the story.
Fox was apparently so impressed with the final product that they offered to release it theatrically, but Bluth begged them not to, saying that all of the corners they cut would be too noticeable if the film was blown up that big.
Word of God: Despite how obvious it is, this film is a prequel to the film Anastasia taking place hundreds of years in the past (if you understand Russian history), which is why most of the story revolves around Russian fairytales and folklore such as Baba Yaga.