If you and I, the president, congress, and the judiciary agree, then yes, and that's kind of the situation regarding the laws around starting a war.

Why only these local institutions? What makes those special?

They have the power to enforce laws

So do the mall cop and the ICC. Why does this arbitrary level in-between matter?

The mall cop much more so than the ICC

That sure is an attitude that explains why US soft power (and with that, Empire) has been crumbling at an unprecedented rate.

You might not care about the rules, but the rest of the world takes notice. This is how you break a world order carefully designed to further your own interests.