Just moves the goal posts to overthrowing the goal of the AI right? "The Moon is a Harsh Mistress" depicts exactly this.
Have you read The Moon is a Harsh Mistress? It's ... about the AI helping people overthrow a very human dictatorship. It's also about an AI built of vacuum tubes and vocoders if you want a taste of the tech level.
If you want old fiction that grapples with an AI that has shitty locked-in goals try "I have no mouth and I must scream."
That scenario seems to value AI goal-instability.