My impression is that during the rule of the Ottomans and up to the establishment of the state of Israel there were sizeable Jewish minorities in Egypt, Iraq, Syria/Lebanon, Yemen, and Libya. Why weren't they keen on immigrating to the holy land? Was it outlawed?
And since there was presumably a minority of Jews living in the holy lands, how did they view themselves and why didn't they try to create a state or a khedivate/wilaya/autonomous province.
I ask specifically about the Ottomans because Jews living in the Middle East could have, if they had freedom of travel, simply pack up and go to Palestine/Israel without having to worry about the language barrier or such.
As for why the Jews did or did not move to biblical historical locations at that time I cannot attest, but in my studies about the development of sectarianism in the Ottoman Middle East I found that it was one of the most religiously diverse Empires/states ever to exist. There were contingents of Druze, Jews, Christians, Shi'as, and various Sufi orders all living under a Sunni Muslim governance. The Sunni government for the most part let these communities of religious minorities run themselves, and if their was a dispute between religions, the Sunni Islamic fatwas held the highest authority. This didn't seem to be an issue that often as most of the minority groups lived in their own self-contained communities. This might be a reason that Jews weren't trying to start their own Jewish state or migrate to one of their holy sites; life wasn't so bad as a religious minority in the Ottoman empire, and for the most part they were able to live freely along their own Jewish orthodoxy. My studies focused mainly on various Islamic sects, so I could easily be missing something there.
Another striking trend I noticed was that the concept of orthodoxy didn't really apply back then. How you practiced your religion was so entirely dependent on where you lived and what religious practices had percolated into yours. The Ottoman Imperial guard, called the Janissaries, were raised by Bektashi, who practiced a religion with elements of Shia and Sufi practices. These Bektashi supposedly gave the Janissaries magical protection in battle, a concept that modern Abrahamic religions would probably find blasphemous. The Mevlevis, another Sufi dervish order were the ones chosen to gird a Sultan with a holy sword upon his ascension. Anyway, I found instances of Jews and Sunnis venerating Shia Imams from Twelver Shia religion, and just generally noticed that religions were much more fluid in those times, with much less focus on orthodoxy than seems to be the case with modern Islamic faith.
If you're interested in this subject I recommend starting your reading with The Shiites of Lebanon Under Ottoman Rule by Stefan Winter.