The ICC should also not be confused with the ICJ. The ICJ, which the United States does recognize, has ruled heads of state are immune for all acts performed during their time in power, including torture, genocide, and crimes against humanity.
No one concerns themself with whether Germany or Göring recognized the legitimacy of the Nuremberg International Military Tribunal. His neck was destined for a noose either way.
The idea that anyone is going to arrest Putin is preposterous.