There are many signatories who are obliged to arrest anyone with an ICC warrant: https://asp.icc-cpi.int/states-parties
If I remember correctly, a former president of the USA cancelled a visit to Switzerland because they were wanted for war crimes. Would Switzerland have arrested that former president of the USA? Hard to say: cancelling the visit was an easier solution for the people who made the decision.
In Britain, an Israeli general arrived by plane but never disembarked because of an outstanding warrant for war crimes. Would they really have arrested the Israeli general? Hard to say: not letting them disembark was an easier solution for the people who made the decision.
Wasn't there the same pitfall with the League of Nations?