>a whole bunch of reasons why the permanent seats aren't representative
You're spot on that they aren't representative of the world's interests, but that's because this isn't what the security council is really for.
Taught in geopolitical terms, the UN is the latest iteration of a number of bodies that seek to protect a small alliance's interests in the long term.
The UN was founded by the winners of WWII, in the brief moment of time they could credibly claim that they represented the broader world's interests. Since then, the WWII allies - US/UK/France/Russia/China - have maintained their disproportionate positions to protect their own interests.
The Security council exists for them - it is the only body that can pass legally binding resolutions, it gatekeeps access to the general assembly, and those 5 golden keyholders can individually veto any other UN action.
These kind of bodies (UN, League of Nations, Peace of Westphalia) etc are often couched in ideals and often do have sub-bodies who do excellent work, as the UN does, but in reality, at the highest levels, are actually consider the spoils of war: the right to dictate your position as a lasting member of extraterritorial governance and protect your doctrinal and national interests.