Okay, but invert that hypothetical. The American President orders a lot of people killed, including sometimes U.S. citizens. More commonly, they order things that result in significant loss of life, which could be prosecuted as negligent or reckless homicide.
Should former presidents be subject to prosecution for those decisions? Remember that criminal laws are often extremely broad, and you can use conspiracy and other legal theories to make someone liable who didn’t perform the actual killing. Heck, part of the J6 prosecution against Trump somehow involves an Enron-era document shredding law.
What I feel like the dissent misses completely, which is quite ironic given Justice Sotomayor’s history in private practice, is that not having any sort of immunity means trusting every prosecutor in the country with pretty much unrestricted discretion to stitch together vague criminal laws into criminal charges against former presidents. Why should we place such trust in prosecutors?