The phrase "insatiable need" means a strong, never-ending desire that can never be fully satisfied, no matter how much is obtained or fulfilled. Full definition
If this were a multimedia presentation, I would now flash up a picture of our lives — our mindless and fruitless preoccupations, our depressions and ragings over not getting our way, our ceaseless and insatiable need for more and more and more, our boredom and blaming. (religion-online.org)
Far too many stories about teenagers — particularly about teenage girls — focus on their apparently insatiable need to be validated by a romantic relationship. (awardscircuit.com)
We all tend to think of yogurt as a health food, but over the years, many yogurts in the grocery store have gone from healthy to hazardous because of America's insatiable need for sugar! (themilitarydiet.com)