Unlike yourself, I've never had the benefit of visiting the region but have done a reasonable amount of reading around it and whilst I certainly can't claim any expertise on the subject, what you've written pretty much matches my own understanding.
I totally agree with you that, had the state of Israel not been created, there would still have been conflicts in the area between different factions and plenty of evidence to support this when you look at many countries today in the Middle East. For some bizarre reason, too many in the West seem to lump all Muslims together, ignoring the differences and frictions between Sunni and Shia for example. Surely that's a bit like lumping all Christians together-they might generally get along far better now than they once did but there is a long history of conflict between Roman Catholics and Protestants for example.
As ever, the British Empire had its role in helping sow the seeds of future conflict in the region although the history of Jerusalem itself is convoluted enough as it is! I think that, post WW2, the Americans have more than played their part too. With the country pretty much exhausted, Churchill was keen for Truman to take over the mantle of protecting Western interests in the region, especially from the newly powerful Soviets. The amount of money the US has poured into the growing state of Israel over the years since is quite staggering.
There did seem a point in time when the changing attitudes of younger generations on both sides seemed to suggest that Israelis and Palestinians could live more peacefully together but very sadly things haven't worked out and, as you say, extremists on both sides have grown more extreme. Echoes Kett's earlier post-the majority of ordinary people would likely just want to get on with their lives and rub along but it's the few who want power and influence who drive things and make things worse by exploiting divisions for their own political or religious ends.