The idea of the Rabbanut (meaning the government agency) was to keep the Hareidim in line, since if Jews followed traditional system, the Gadol Ha-Dor (who was unlikely to be pro-Zionist) would be the de facto leader of the Jewish community (and the thought of the Hazon Ish or the Satmar Rebbe having serious influence was terrifying – remember the Zionists had to shoot Jacob Israel De Haan who was the shliach of the gedolim). The fact that most Shomer Shabbos Israelis support the regime, and serve in the army, shows the Rabbanut has fulfilled its primary mission. While there are Gedolim in Eretz Yisrael, they have little or no involvement in running the political system or the economy, and for most Israelis, the Zionist dream of a nation free of the yoke of Torah has been realized.
To eliminate the secular stranglehold on Israeli life it would be necessary to convince the seculars to emigrate (perhaps as part of a peace agreement in which the goyim pay them oodles of money to relocate, combined with agreements of western countries to accept them as immigrants). It should be noted the emigration of secular Israelis is common, and many are well established in their new homelands.. In such a scenario, the idea of an autonomous Jewish homeland, dominated by Daas Torah, could co-exist with a Palestinian/Islamic state on the theory that Haredim don’t feel the need to run the government. If would be similar to the pre-zionist status quo when Turkey was the colonial power and Jews didn’t get involved in Ottoman politics. An advantage of being part of an Islamic state, even though it would mean limited civil rights for Jews, would be the prohibition of abortion and other toeiva (note the such bans would be an anathema to the Zionists).