Is Aoraki/Mount Cook worth adding to a South Island route?
Aoraki/Mount Cook is worth building around if you want the alpine version of New Zealand. Just do not make it a single perfect-weather assumption; clouds, road time and track conditions can change the payoff.
Answer
Aoraki/Mount Cook is one of the places where the South Island stops being merely pretty and becomes severe: broad valleys, cold light, big ridgelines and walks that make the road feel justified. It is also a place that can vanish behind weather. That does not mean you should skip it; it means you should not give it one fragile hour between Tekapo and Queenstown and expect the mountain to perform. Stay nearby if alpine scenery is a priority. Use Tekapo or the Mackenzie Country as part of the approach if the route fits. Aoraki is worth the space, but it does not reward an itinerary that leaves no margin.