As said by others in the comments, there are quite a few things that come into play here, which all would be true regardless of who the actual sitting President is.
The Constitution of the US is seen as the Supreme Law of the Land. The US being subservient to the ICC would be a direct violation of that. The ICC does not and cannot carry any legal weight in this country.
There are already laws in place saying that the US can and will use military force in order to extract a US citizen held by the ICC.
The US is, by far, the most powerful military in the world, and it isn't even close.
The US is also the cornerstone of the global economy. Any attempt at enforcing sanctions against the US in order to force compliance with any kind of international law would likely simply be ignored, and would probably do more damage to the sanctioning country than to the US anyway.
The US is host to the United Nations. I don't think I have to say what kind of shitshow would happen if the UN tried to arrest the leader of the country that's hosting it.
The ICC could issue a warrant for Trump's arrest as a symbolic gesture, but it would have about as much practical effect as if I had issued it.
They have already not done this with Putin or Netanyahu.
There is a less than zero chance they will do this with a sitting American president. No one's coming to save us from him we're going to have to do it ourselves.
Hmmm what would the Secret Service do if Trump were to be arrested while on a diplomatic trip? Yeah, Trump would not be taken into custody, I’d bet my Legos on it.
It matters, just not in as much as one might hope. It is mostly a symbolic step, true, because no one will arrest a sitting president. But it shows that the court is observing and condemning the actions. Think of what might come after: Trump couldn't enter quite a few countries without fear of arrest once he is no longer president. Same with Putin, or Netanyahu. It makes international action so much easier if you can just say "well, there is a warrant out for you, so you better not show up". Become a refugee? Better not go to a country that might uphold the warrant. Regime change in your current country of residence? Better think fast, the new administration might just need a reason to take you in.