The League of Nations was doomed to an absolute collapse from the word go. It didn't stand a chance in heaven of succeeding, as not only did it lack key countries, but also for the reason that it was incompetent and unorganised.
The two countries which would have benefited the League of Nations the most, had they been a part of it, were America and Germany. America at the time was the most powerful country in the world and was seen as the epitome of what a country should be. It was, after all, the American president Woodrow Wilson who fabricated the League into being. The morale of all nations who actually joined the League would have been much higher had its founder actually taken part.
As for Germany, we must not forget that the League of Nations is held together by and is made to enforce the Treaty of Versailles.
A large percentage of the treaty solely focuses on how to punish Germany for World War 1, but also in the treaty it states that Germany is not allowed to enter the League of Nations. It would have made a lot more sense for Germany to be forced to enter the League so that it could have been kept a close eye on. The treaty of Versailles was also a liability to the League as it would always be associated in conjunction with it, especially by the Germans. This shows that should the treaty of Versailles be attacked or destroyed it would drag the League of Nations down with it.
The League was incompetent as its powers were weak, and it had no army with to enforce its authority. What the league basically did with a country (country X) that was being ill-disciplined was to sit down with...