My choir director always discourages us from singing "I" as "I" because it comes out "IIIAAAEEEE." Say it and feel how much it lifts your jaw and narrows your palate, pushing everything to the front of your mouth. If you drop your jaw, it comes out more "AHHH." It's still understood, but sounds better.
"And the postman sighed as he scratched his head, you really rather thought she ought to be dead..."