These principles are not objective moral axioms that we can all reason from.
We decide, as sovereign countries, what they mean to us, how they should be implemented, or even if we (as a country) don't value this or that. There is no magical tablet of Rights that we can spiritually commune with to determine "X is a right but Y is not." These are all politically and culturally determined.
So it absolutely matters, very, very much who decides, and millions have died as a consequence of those decisions. It does not make much sense for anyone to hand those decisions over to the ICC. Unless and until we have a single global culture and moral framework the whole idea is absurd...except as a vehicle for the power plays of different factions at the international politics level.
Because they are politically and culturally determined, because they are not something that people are just born with the innate ability to find, is exactly why handing decisions over to people belonging to different cultures/societies/institutions is highly dangerous. The only way to actually protect our rights is to not accede to institutions like the ICC. It's absurd to say that because billions of people could be trained to believe in things they don't believe in we must act as though the things they don't believe in are universally true, or else we will lose our freedoms. We can simply live in sovereign countries that do hold these beliefs - and as for the countries that do things we find revolting, we can pressure them or ignore them or war with them as we see fit and as has been done since the dawn of time. But ultimately you have to accept that different cultures have different values, even if you're one of those that want to do something about it. You can't just stick your head in the sand and pretend the ICC actually adheres to these ideals.