That is specifically why I don't permit an executive. This isn't one army, it's an alliance of armies. They were (in my original proposal, not in the comment above) controlled by a council of heads of government who had to take (arrest) suggestions from the chief prosecutor of the international court, but were forbidden to take other actions collectively.
In fact, I recall suggesting that such a group of allies would promise to use force only to defend direct attack on their own borders, and to execute arrests.
> We're organized as nation-states in the first place so we can protect (generally) and pursue interests based on some sort of shared goal or value.
I'm not sure I was ever offered a choice of whether or which nation to join, nor given any arguments for it. The reason(s) for their formation are certainly not rational - they are an emergent phenomenon!
> the UN
The UN is a diplomatic mission, which aims to give nations who come into conflict a neutral space in which to talk to one another like grown ups (or, often, not like grown ups.) It is a fundamentally different goal to an organisation which aims to use the traditional enforcement of rule of law to coerce those with political power to act within at least some behavioural boundaries.
> Coming to an understanding between 8 Billion on who should be able to arrest them is extremely difficult.
Actually, again, this hypothetical force only has arrest power over international crimes - specifically, crimes which are committed by people wielding state power. This includes members of governments, civil services, uncivil services (police, army), and so on, but most definitely not civilians.
(An interested edge case I considered was the idea of an impromptu Texan militia who attempted to invade Mexico. I can't remember whether I decided they had designated themselves a pseudo-state or not by doing it. The same reasoning about whether jurisdiction should apply also works for most terrorists, anyway.)