That's not their intent in Putin's case really:
"Today’s arrest warrant will limit Putin’s diplomatic options, and it will make it harder for anyone to dismiss Russia’s aggression against Ukraine as a “territorial dispute.” The real point of today’s ICC arrest warrant is to bring the world to a moment of moral clarity that what Putin is ordering in Ukraine violates the law and moral values of civilized nations around the world. "
The Russian president and the Russian commissioner for children’s rights stand accused of the war crime of abducting Ukrainian children, and more charges may follow.
www.atlanticcouncil.org
Or perhaps the hope that if some time in the future if Putin is ousted, they will turn him over to the Hauge in the way that Milosevic was ( a longshot put there it is)
en.wikipedia.org
It's as much a political statement as it is anything else, and politics do matter, like it or not.