In the Torah and Chazal, there is a concept called "נשיא". The נשיא can be either the king or [in the language of Chazal] the head of the Sanhedrin. There is also the נשיא of each tribe.
Years ago, there was a Gadol Bi-Yisrael, a real גדול בתורה, who published a tshuva in his sefer: The question was - Do all of the Halachos that apply to a נשיא, also apply to the President-נשיא of Medinat Yisrael?
That was it. He was out. He lost almost all of his prestige. That is why you probably never heard of him. מה לנשיא מדינת ישראל ולראש הסנהדרין והמלך??? The President of מדינת ישראל is an honorific title given to a person who cynics say [it is definitely not good to be a cynic but sometimes it is worth listening to what they have to say...] has two jobs. 1] To get Kavod. 2] To get a big salary. That's it.
The whole government of Medinat Yisrael was established with the express goal of creating an environment where Eretz Yisrael would be the place for the new, "liberated" Jew, unencumbered by Torah, Halacha and Tradition. That was the dream of Ben Gurion and his cronies. That is why [among other things] the law of the land is based not on Jewish tradition but an amalgam of secular systems of law - British, Turkish etc. [with some Judaism sprinkled in].
So you have this guy, not even elected by the people [but by the Knesset] who is often a מחלל שבת בפרהסיא אוכל נבילות וטריפות to mention just a few of his good qualities, who has no political power, elected by a body of people who are composed of many secular even anti-religious people, including a few Arabs, to a ceremonious position. [It is like a person who receives an honorary doctorate. Don't go to a surgeon whose only degree is an "honorary doctorate"]. Then a very venerable rabbi conducts a serious discussion as to whether when he dies, everyone including Kohanim become Tamei for him and everyone rips Kriyah and all the other דיני נשיא apply to him.
Ahhhhhhhhhhhhhh. That was tooooo much. Had it been categorized in the "Purim" section of the sefer, that may have been a saving grace. But, alas, it wasn't. And so ended this Rav's legacy as a Gadol.
Too bad.
I say this in order to bring home the point that our heroes and models are Tzadikim, אוהבי ויראי השם, Talmidei Chachomim, Baalei Chesed Vi-tzdaka etc. etc. When I think of a guy like Herzog, I hark back to his grandfather, the Rav Ha-Roshi Rav Yitzchak Isaac HaLevi Herzog ztz"l, who was a tremendous Tzadik, a man of nobility and self sacrifice and an auto didact in כל התורה כולו [not to mention his vast secular knowledge].
HE was a נשיא בישראל, not in the pure Halachic sense but as a leader and guide. "נשיא" means elevated - and that he was.