Are Lake Tekapo and the Mackenzie Country worth an overnight?
Tekapo can be beautiful, but it is easy to overweight because it photographs well. Stay if the route needs a calm alpine break; pass through if it is only another lake between bigger commitments.
Answer
Lake Tekapo and the Mackenzie Country are at their best when they slow the trip down: pale water, big skies, dry hills and the sense that the South Island has opened out. That can absolutely be worth an overnight, especially if you need a softer step between Christchurch and Aoraki/Mount Cook or Queenstown. The caution is itinerary inflation. Tekapo photographs so well that it can steal a night from places with more to do in poor weather or more varied walking. Treat it as a mood stop, not a compulsory monument. If the route is already full, passing through may be the cleaner choice.