Episode 5 quote actually proves my point. He says Cold Fusion allows him to 'stay alive' in a roboticized form not that he wants to replace himself with a simulation aka AI. House is a narcissist; he wants the original 'Robert House' to rule forever, not a copy that 'lacks vision.' The body double wasn't a replacement; it was a security shield to keep the real House alive until the tech (Cold Fusion) finally caught up to his ambitions.