I never understood the idea of having a global that is organized like a democrat (sorta) legislature having member states who are not democracies.

If we did that, all the internationsl charters and agreements based on the UN would be dissolved, and we would never be able to create anything better in its place, unfortunately. No more human rights, children's rights etc. And while there are tons of issues with the UN and weaknesses to its systems I still think it's better than nothing.

Do you really think it would be easier to start from scratch? The UN as it is, with all it's history and authority, has trouble agreeing on the exact wording of a letter.

You get rid of the UN, you're actually just going to have no international law, and a medieval-style free-for-all. Not to mention it's secondary purpose, which is just as a place where everyone can talk to everyone, even their enemies.

why is it headquartered in the United States?

IIRC, because the Soviets though it would end up being a joke and said "yeah sure, you can have the HQ for the new League of Nations".