Absent the USA being an active member of the League, it was essentially dead on arrival. The other problem is, like the international court at the Hague, there is no enforcement mechanism. On the other hand, because the membership of the League was much smaller than the UN, there was at least the potential for some level of success. I mean with about 135 members (not counting observers like the Palestinians) and countries like Naaru having the same vote as the USA, China, etc getting the UN to agree the sun rises in the east and sets in the west is a major accomplishment.
In the end the problem with the League (and the UN), is that the differences in philosophies, goals, strategic imperatives etc between member nations is usually much more important than agreements between them - and this is just between the serious/important members. Add in the pissant countries whose votes can be easily obtained by threats or purchase.....
Organs like the WHO and UNICEF do/did well when they were basically non-political, but even they have been politicized and rendered less or ineffective.