Why the Recent ICC Warrant Against Putin Will Accomplish Nothing

The ICC has issued a warrant for the arrest of Vladimir Putin for the crime of resettling Ukrainian children in Russia, will this have any affect on the war? Will this damage Putin in any way?
Is this a legitimate complaint or propaganda tactic and now that the ICC has set a precedent of serving an arrest warrant for the leader of Russia, will they finally bring charges against Tony Blair and George W Bush for the Iraq war?

Links:
AP article on the ICC Warrant
https://apnews.com/article/icc-putin-war-crimes-ukraine-9857eb68d827340394960eccf0589253

AP article on the alleged child abductions
https://apnews.com/article/ukrainian-children-russia-7493cb22c9086c6293c1ac7986d85ef6

France 24 article from 2018 about the US threatening the ICC if they attempt to charge Americans for crimes in Afghanistan
https://apnews.com/article/ukrainian-children-russia-7493cb22c9086c6293c1ac7986d85ef6