The objective of the ICC is to provide a framework to enable prosecuting and punishing the people ordering particularly egregious acts in a way that is more consistent with liberal rule of law principles than post-hoc tribunals like after WW2 and that is more accessible to fragile / new countries due to having the legal infrastructure set up and at least partially legitimized by it being an international body
The fact that Putin (for example) might at some point get extradited / captured, prosecuted and jailed for whatever crimes he gets found guilty of is a moral good in and of itself
If this being done at the ICC rather than in an Ukrainian or Russian (in an hypothetical regime after Putin's) helps others accept the verdict as more based on fact than politics then that's why the ICC exists as an entity
If this makes someone down the line think twice about ordering war crimes then that's an added benefit but it's not the point
Putin & the Israeli warrants are a bit for show since it is very unlikely to result in an arrest (although it does serve to isolate both, which i suppose is a punishment)
However don't let that take away from the other work the ICC has done. They have thrown people in jail.
For the palestine situation, hamas leadership has generally fared poorly (no tears from me, they started this war after all). However you can't issue a warrant for a dead person.
It should be noted that the ICC has not as of yet alleged that anyone has comitted genocide in palestine. All the (public) accusations thus far have been for lesser crimes. There is a big difference between what randos on social media are alleging and what the ICC prosecutor is alleging.
Furthermore, everyone has the right to be pressumed innocent until proven guilty. That includes people accused of heinous international crimes like genocide or crimes against humanity.
(To date, the only person the ICC has ever accused of genocide is Omar al-Bashir from Sudan)
If for example Putin was overthrown and had to flee Russia, and happens to fly over an ICC signatory, he could rightfully be arrested and brought to justice. What is the alternative? CIA assassinations and kangaroo courts?
He could be arrested and brought to justice regardless, the ICC provides literally zero value-add here. Sovereign countries will do what they want regardless of the ICC's rambling, and they never needed the ICC to justify their actions to begin with.
They have a warrant out for Putin, has that made any impact on the war in Ukraine?