Mary Poppins doesn't stay confined to the viewpoint of one character. At the beginning, we see Bert and he speaks directly to us, telling us a little bit about the Banks Family and leading us to their house. But if you thought Bert would remain as the narrator for the rest of the movie, popping in from time to time to say stuff to us, you were wrong.
The movie features scenes containing only Mrs. Banks and the maids, only Mary and Bert, only the children and Mr. Banks, and Mr. Banks facing down the bank partners on his own. It doesn't remain squarely focused on one character, but gives us a picture of how the story weaves its way through different lives.
But, the story doesn't make any crazy shifts in time and place—it doesn't suddenly shift to 500 B.C. Finland, or show us what Mary was like as a girl. It keeps itself confined to the present in 1910 London (aside from the trip inside the chalk drawing—though that drawing is itself located in London).
But the movie's structure is beholden to Mary P. She's the one who instigates the story, and sets adventures rolling. The structure of the movie is basically:
Mary shows up.
She does some crazy stuff and takes the kids on wild adventures.
This annoys Mr. Banks.
Banks gets fired due to circumstances Mary helped orchestrate.
He lightens up and spends time with his kids.
Now there's no need for Mary anymore. She can leave.
That's not a convoluted narrative. It keeps things simple yet elegant, without too many (or any) subplots.