Hashem wanted the nations of the world to recognize the greatness of the Jewish nation. Abraham was held in the highest regard by the nations of the world. Isaac’s prestige was diminished relative to Abraham’s, and Jacob’s prestige even more so than Isaac’s. Ultimately Jacob’s children were enslaved by their hosts, the Egyptians. Had the Jews been respected it would have been very difficult to enslave them. Hashem wanted to ensure that His chosen nation would receive the respect that the Am Hashem deserves. This was accomplished through yetzias Mitzrayim and the first kabbalas haTorah soon after the exodus. The nations of the world were gripped with palpable fear, Chil achaz yoshvei plashes (which Rambam says refers to the events at Har Sinai and not the splitting of the Red Sea). All the nations recognized the greatness and uniqueness of the Jewish nation as Hashem restored the honor of Bnei Yisrael. The kolei kolos announced that Bnei Yisrael were truly special, Hashem’s chosen people.
After the destruction of the Beis Hamikdash, the Jews again lost the aura of respect. The honor of Am Hashem had to be restored. Hashem told Isaiah that in the future, the people will perform an act of Kiddush Hashem. Chananiah, Mishael and Azariah restored the honor of the Jewish people years later by making their stand against Nebuchadnezzar and reminding the people of the mitzvas Kiddush Hashem. Nebuchadnezzar’s forcing them to bow down before the idol was Hashem’s plan for restoring the honor of Bnei Yisrael, through their act of defiance.
The mitzvah of Yeihareg V’al Ya’avor includes the concept that the honor of Yisrael should not be diminished. That is why Rambam includes the different forms of Chillul Hashem – idolatry, illicit relationships, murder or a scholar who acts in a way that brings shame on Torah and himself: all of the above share the common property of diminishing the honor of Bnei Yisrael. According to Rambam, when a Jew worships idolatry, even under coercion, there is still an aspect of Chillul Hashem because he has diminished the honor of Bnei Yisrael.
Borrowing from various ideas of the Rav, zt”l, I would add that the establishment of Medinat Yisrael was so very important to us in that it re-asserted our historical significance and, often grudgingly, respect for the Jewish people. They may still despise us, but at least they respect us as well. After the Holocaust and the destruction of our people, Medinat Yisrael was a clear message to us, kolei kolos, that we were still Hashem’s chosen nation. Christian theology maintained that the Jew and Judaism were rejected by God, symbolized by the destruction of the Temple and the exile of the Jewish people. The re-establishment of the State of Israel, with all its issues, and the respect it accorded the Jewish people who had just suffered through the Holocaust and were despised and bereft of hope and support, showed us and the religions of the world that Hashem has never rejected us and our faith in the coming of Messiah and the ultimate redemption is well placed.