Agreed with Schmitt.
FWIW, the "I was just following orders" excuse doesn't work in modern international and US law. This goes from every person actively involved from the person who pushed the button all the way up the chain of command.
While Admiral Bradley is clearly on the hook for this, the missile operator may not be if they were unaware that there were survivors clinging to the target. If Secretary of War Crimes, Whiskey Pete, gave a "Kill'em All" order, he's on the hook too. If Trump told Whiskey Pete to "Kill'em All", then he, too, is on the hook. Due to SCOTUS, Trump may be absolved of US prosecution, but not from the ICC. As President, he might be protected by diplomatic immunity, but once he leaves office, he might not ever be able to leave the country without risk of arrest and prosecution as a war criminal.
I'm not a lawyer, but as many have pointed out, all military personnel are indoctrinated on the laws of war and lawful vs. unlawful orders. Junior personnel often need to be reminded of those laws since young people are easier to manipulate when it comes to following the rules vs. "this is how we do it in the real world, kid".