The League of Nations had proud aims but was doomed because it was based on the Treaty of Versailles which most nations signed but disliked. It hoped to aid disarmamnet so stopping wars therefore making the world a better and safer place by improving citizens' working conditions, and by preventing disease. But the US, among other countries wasn't convinced. The organisation consisted of an assembly meeting yearly and a more frequent council for considering crises. A small secretariat was to manage paper work. The Court of International Justice was seen as necessary and many committees (eg International Labour Organisation,Health Committee) were put to implementing humanitarian work. This was not seen as doable by the US which also saw other weaknesses as well as strengths.
Its main strengths was that it had set up by the Treaty of Versailles, which the nations had signed but didn't like, and there were 58 nations members by 1930s. However the US was not happy. The league had no army to enforce its will, (and anyway the US only had faith in or needed its own) and though it could give arbitration through the Court of International Justice, or apply trade sanctions against countries that went to war this was not seen as powerful enough.
Many other nations disliked the Treaty of Versailles and considered that its aims were far too ambitious. Not only that, but Germany and Russia were not members either. The League's its adminstration was seen as way too heavy impractical and onerous and also decisions were going to be made unanimous only.
Although you wrote an in-depth post, I think you missed the point of why America refused to join. There are a variety of reasons of why the United States refused the join. For instance, the American Senate was afraid that by joining the league could create greater obligations that essentially transcended American interests. This means a loss of sovereignty for them which at the time was a big deal because they could have been possibly put at the mercy of the European agenda. So ultimately one viewpoint is that Americas refusal to join is linked to the fear of a loss of power over U.S. internal/external affairs by the American Senate. However, there are also many other reasons I cover in depth in my blog post in my source link. Check it out.
The two main reasons that the United States did not join the League of Nations are because:
1. Woodrow Wilson, a Democrat, believed that he did not need to bring anyone from the Senate, which was Republican (led by Republican Henry Cabot Lodge), to the Paris Peace Conference with him. He planned everything himself, making his goals public without the consent of the committee. The Senate is in charge of approving treaties, and because they were bitter about the Treaty of Versailles, they rejected signing it, which in turn rejected the League of Nations.
2. The United States also practiced a policy of isolationism, the belief that they should stay out of foreign affairs. The League of Nations called for collective security, that when one nation harassed another, all the nations would act. The United States at that time did not want to be connected to other nations' affairs.
The league was heavily linked to the Treaty of Versailles, and many nations who signed it did not agree with its content. America was one of those nations. There was also a problem with the cost of joining. The League did not have an army to enforce and it seemed as not powerful enough.