Indeed, but weren't they divided?
Yes. One of the Palestinian Arabs' biggest problems was that they were completely disunified, organizing mostly along tribal lines and having not dominant leadership. They weren't even united in being against the Zionists; several towns and tribes supported the Zionists, even in the war.
Without foreign intervention, there still would have been conflict, but it would have been more like extensive riots than a proper civil war, probably. Ironically, the Palestinian Arabs might have ended up with more of their notionally allotted land (and Jerusalem might have actually become a UN zone!). On the other hand, the Palestinian Arabs could well have ended up just as expelled, but also from the West Bank and Jordan.
Also I suspect David Ben-Gurion wanted this war for nation-building purposes, since
Jewish immigrants were quite a motley crew back then.
The Zionists were actually very unified in spirit at the time. There were some political disagreements - notably over how much to cooperate with the British and the Arabs - but all Zionists in Palestine considered themselves to be part of the same nation, more or less. While some of the Revisionist fringe might have wanted a war (probably for no more reason than the lulz - the Revisionists were very violence-happy and had a big warrior machismo thing going on), the Labour Zionists were too smart to want a war, especially after '45, when the British made it clear that they would back Jordan, and Jordan made it clear that they would take a close interest in any conflict in Palestine.
This said, at what point at the latest should these financial incentives have begun
to make an impact? How would they have affected British attitude on immigration?
Changing demographics would have reduced tensions, wouldn't they?
I don't think it would be possible to solve the problem. The felaheen were having "their" land sold out from under them by landowners in Beirut and Damascus who didn't give a shit. The Hebrew Labor movement limited their ability to get "contract" work from the Zionists. The incredible wealth flowing into Palestine brought immigrants from other parts of the nearby region, as well, further making it difficult for displaced peasants to find work. I can't imagine any workable method where people would voluntarily relocate for money, especially in a tribal, agricultural society where people feel a deep connection to their ancestral holdings.
Ironically, I do think that looser British immigration policy would have reduced violence. The problem with Palestine was that the British were very good at balancing the power, mostly by using the Jews to help keep the Arabs in check, and keeping the Jews in check by choking off immigration. With unfettered immigration we're looking at a much larger Jewish population even before WWII, and one that's maybe
much larger after (twice as large? Hard to say; the Holocaust still probably happens to some extent, but is it 5 instead of 6? 4? 4.5? 3? These different numbers all mean very different things for future Israel). While a larger Jewish population might lead to a short term surge in violence, in the longer term I think it will become clear that the Arabs can't force anything, and there might be a Jewish majority in the whole region. This might not lead to an immediate drop in violence, but more Jewish "police" presence will eventually have its effect, and a sufficiently strong Israel might not be attacked on its birthday (or it might, who knows)