If the league needed an army then they would need to ask a country to lend them troops, if there were casualties (and there always are casualties) the the president of the country who lended them the army would be responsible and would need to take all the blame from the families of the casualties so it might then reflect on their elections or the amount of support he has, so no country would want to lend their army because it is in the interest of the politicians to keep their army safe
The league also could not succeed because the power that the league had was not enough so the league could not deal with major powers because the major powers would probably just ignore the commands of the league. Another major reason why the league would fail is because the two countries in power, which were France and Great Britain, is because they have self-interest and would act in a way that suits them the best, for example the incident between Japan and China in Manchuria, you can see that Great Britain, especially, proceeded so that there would not be a conflict with Japan, because England had colonies in Asia and Japan had a very good navy. If the league would have upset Japan then they might have invaded the colonies of Great Britain. .
However, you can argue that the league was not doomed from the start. The league has provided some racial equalities, for example the members of the league were mostly european diplomats but there were also Japanese diplomats the participated in making decisions, so the league has combined several different nations into one whole organisation and the collaborated and cooperated. If the league focussed on problems that are worldwide but not as serious as war then they would have succeeded this was proven by the league solving the problems with refugees, when half a million of prisoners of war were in Europe after war and the league appointed an expert organiser an explorer (they chose an explorer because they are really organised and when they go to explore they plan all their moves) so Fridtjof Nansen (the explorer) displaced 450,000 to their houses or found them new homes.