You can ridicule this idea, but we're already having the US (partly through NATO) taking the role of a global sherif, except without aiming for neutrality, accountability, nor justice, so we end up living in a geopolitical world in which "might makes right". If we continue like this, we will have another World War, but learning by mistakes is sometimes the only realistic way forward.
No. What I'm proposing is to make these processes purposefully and explicitly neutral, accountable, and just. This implies democratic and decentralised governance and decision-making. Clearly this isn't happening now.
As long as you’ve got humans in the mix, it’ll also be political. What you’re describing is a political organization and wishcasting that it’ll be as neutral as you envision according your values of neutrality. It’ll also be the most powerful political and military organization on Earth, so in other words, same shit as we have now, different letterhead. You may as well be describing America, you just don’t want it to be America, and I can respect that perspective even if I don’t agree with it, but your hypothetical organization is not as different as you think it is.
It's 100% different. The institution I envision should represent all countries, or at least member countries, so that it has global democratic legitimacy. Simply put, interests of one country are not equivalent to interests of all countries. If one country tries to take the role of that institution, sooner or later it will run into a conflict of interests.