There is no theoretical limitation inhibiting AI from eventually taking over every job reliant on intelligence.
I already see people not hiring artists of their own because Wombo.art gives them “paintings” for free. I have no doubt there’s already thousands of works that use 15.ai instead of hiring voice actors who may enjoy their work. When it comes to the point humans can no longer compete with AI in these spheres, they will be pushed out of the market, for daring to charge such hefty fees for their labor compared to the pennies needed to run your AI pet.
So, even if AI somehow wasn’t to take over programming also, the above still indicates a deep societal problem: that it will be accepted at all.