The question is going to get different types of answers because of its vagueness. This might not be a bad thing because it opens up discussion. However, it is going to be difficult to get "one exact answer" because so many different variables can be interpreted. One example of this ambiguity would be in what it means to "live up to the ideals." The nature of the wording makes it impossible to derive an exact answer. Any time ideals are introduced into an equation, this means that there is a standard which is deliberately set so high that it is impossible to achieve. Nations could never fully represent ideals of anything, so this would mean that all are going to fall short. At the same time, when terms like "world powers" are introduced, different understandings can result. In this regard, answers will vary.
With this in mind, I think that a case can be made that world powers like the Soviet Union and the US fell short in specific situations. One such instance would be in the ideal of collective action. The First Article of the charter suggests that nations should strive "to take effective collective measures for the prevention and removal of threats to the peace, and for the suppression of acts of aggression or other breaches of the peace." This ideal was not evident in the unilateral action that major world powers took in areas of the world like Vietnam and Afghanistan. In these settings, there was a considerable shortcoming in the pursuit of the ideal of collective measures. World powers had to strive to meet the ideal of enhanced quality of life for all citizens. The Charter states that all nations must strive towards the ideal of promoting "social progress and better standards of life in larger freedom." Certainly, marginalized individuals in the Soviet Union and in the US would display this ideal as something not easily achieved. The fact that both nations featured segments of the population that were not able to experience the full extent of social progress and pursue "larger freedom" would be representative of how the bipolar world powers did not live up to ideals put forth in the UN Charter between 1945 and 1991.