the choice thing is pretty key. but, here's another key point: iraqi jews were in exile. they'd been there once before; maybe it was starting to feel like home. but, the culture maintained the fact that it was not home. palestinians are the hebrews that weren't exiled - the hebrews that converted to islam when the region was conquered. they didn't come from egypt or jordan or syria or the arabian peninsula - or even iraq. they're the indigenous, hebrew population of the region; they don't have a home to go to, because israel is their home.

modern genetics is an amazing thing, and the data is in and has been for a while. the arabization of this area was cultural. the lebanese are not arabs, but lebanese. and likewise with syrians and iraqis - and israelis. the population did not disperse, or otherwise evaporate. some jews fled, no doubt. but the broad base of the population is hebrew. this has been their home for many centuries, they just changed religions along the way. why? for good reasons - economic, cultural, social. and, it's not like there's really that big of a difference in the first place.

the romans changed the name of the province to palestine, with the intent of erasing jewish identity. but they didn't carry out a full genocide, like they did in carthage. and the dna makes it apparent that the dominant population group in the region did remain jewish right up until the british mandate and beyond, regardless of (what is now clear is) great exaggeration in the exile stories.