My guess is that it's simply a matter of how difficult it is to prove the issue. The Putin case was very simply because there is an official state program to do things that are considered genocide. Israel is at least pretending they are letting aid in.

Israel is not pretending. They've let in tons of aid, that is stolen by Hamans constantly. I want to remind you that an American soldier has died during the built of a humanitarian port by the US navy.

But that's what the court itself is for! You get plausibly charged with a crime, you go to court, and the case is determined one way or the other.

What happened in this case is that Israel beseeched its allies to lobby the court not to look into what was happening [0]. And the UK demanded hearings to impede the ICC warrants from being issued (purely politically, as this was done under Sunak and then Starmer/Lammy dropped the objection, but the delays were already underway).

[0]: https://www.axios.com/2021/02/07/israel-icc-political-pressu...