The Balfour Declaration, which put the creation of Israel into play, was created by the British during WW1, at a time when the entire region was under the control of the Ottoman Empire.:

His Majesty's Government view with favour the establishment in Palestine of a national home for the Jewish people, and will use their best endeavours to facilitate the achievement of this object, it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine, or the rights and political status enjoyed by Jews in any other country.

It's obvious that Israel is the strongest and most strategically important ally that America has in the region today, nobody can deny that. Just like nobody can deny that Hamas, the ruling entity of Gaza for almost 15 years, is allied with and strategically important to Iran, Russia, and many of Israel and America's other big geological adversaries. Iran supported Hamas' recent terrorist attack on Israel because they understood that they, an Islamic theocracy, would benefit from the chaos of what appears to some as a religious war. Similarly, Russia wants chaos in the region in a desperate attempt to divert western military resources away from supporting Ukraine.

To me, none of that makes the situation simpler.

As for the clip you've linked, the first Arab-Israeli war was more than 20 years prior to that. And, taken in context, Biden was arguing against the Reagan administration's plans to arm Saudi Arabia, and to that point I'm not really convinced that he was wrong...

As for claims of genocide, I'm afraid that cuts both ways:

The original Charter identified Hamas as the Muslim Brotherhood in Palestine and declares its members to be Muslims who "fear God and raise the banner of Jihad in the face of the oppressors". The charter states that "our struggle against the Jews is very great and very serious" and calls for the eventual creation of an Islamic state in Palestine, in place of Israel and the Palestinian Territories,[3] and the obliteration or dissolution of Israel.

The Day of Judgment will not come until Muslims fight the Jews, when the Jew will hide behind stones and trees. The stones and trees will say, 'O Muslim, O servant of God, there is a Jew behind me, come and kill him.' Only the Gharkad tree would not do that, because it is one of the trees of the Jews.

1988 Charter of Hamas

So yeah, if you think the modern world's oldest geopolitical conflict is simple, then you're either way smarter than everyone else or you're mentally reducing the problem until it confirms your existing biases. Personally I think it's more complicated than you're making it out to be, which is why it hasn't been settled by 100 years of diplomacy and war.

I read the BBC article on the recent shooting, you're right, it's tragic and wrong. Two gunmen shot up a settlement and then started exchanging fire with an IDF unit and the child was shot in the crossfire. This is awful, but has nothing to do with Palestine being an independent nation since this happened in the west bank, not the Gaza strip, which as I understand it, are different.

Also, this article (which is the only one I can access) seems to be posted in bad faith, the whole tragic situation started by a bunch of people opening fire on random Israeli citizens. But there's no mention of this at all when you're decrying Israeli violence. And the same for your talk about "Strategic Bombing", that no one is doing, or the political situation in the west bank (which is different from the Gaza strip).