If AI displaces human workers faster than the economy can reabsorb them, it risks eroding the very consumer demand firms depend on. We show that knowing this is not enough for firms to stop it. In a competitive task-based model, demand externalities trap rational firms in an automation arms race, displacing workers well beyond what is collectively optimal. The resulting loss harms both workers and firm owners. More competition and "better" AI amplify the excess; wage adjustments and free entry cannot eliminate it. Neither can capital income taxes, worker equity participation, universal basic income, upskilling, or Coasian bargaining. Only a Pigouvian automation tax can. The results suggest that policy should address not only the aftermath of AI labor displacement but also the competitive incentives that drive it.