"Focus on creating a valuable product. Expect reduced time and cost as a side effect."

That's what I like to emphasize to anyone that implements Scrum or any Agile methods in general, including myself. When implementing Agile, we need to understand that we are doing it for the sake of creating the most valuable product for our customers. We should be doing it to make room for collaboration, communication, and changes to maximize the benefit of using our product. We're not doing it to cut down resources.

That doesn't mean making efforts to cut down resources are forbidden in Agile. Being efficient is always good. If we managed to do it, good for us. Just remember that efficiency should be considered as a side effect of being Agile, not the purpose.