I agree with your first statement, and not with your second. Israel has been using Hamas to keep the Palestinians divided.

Call me a cynic, but after watching 40+ years (since I first started paying attention) of Israel doing everything to NOT allow the Palestinians to flourish, I do not believe that Israel would have allowed Hamas to improve the lives of Gazans. Israel allowed Hamas to be funded and there is NO doubt that it was Israel that allowed Hamas to get funding (mostly from) Qatar.

Had Hamas turned over a new leaf and really tried to help the Gazans flourish, I'm 100% sure funding would have been cut off, Israel would have found a way to replace Hamas with some other terrorist group, or more likely both.

Your last paragraph is (IMO) spot on.