In the comments to a post a few weeks ago (link), someone pointed out that Yeshivas Merkaz Ha-Rav, founded by Rav Kook, does not have a yeshiva-army Hesder program. It is interesting that its website calls the yeshiva the heart of a movement that includes Hesder, yet the yeshiva itself does not have a Hesder arrangement:
Since its foundation the Yeshivah and all that it stands for has grown in influence until the name "Merkaz HaRav" has come to denote not only a Yeshivah, but a Torah concept which is the heart of a movement. This movement encompasses thousands of pupils and students in high school yeshivoth and yeshivoth hesder, pupils and students in the ulpanoth and michlaloth (girls' Torah high schools and colleges), and members from all walks of the Hityashvuth (Settlement) movement.I am generally unfamiliar with the Merkaz Ha-Rav ideology but I came across an explanation for this. R. Shlomo Aviner compiled lectures by R. Tzvi Yehudah Kook on the subject of army service in a book titled Sidrei Tzava Vi-Yeshivah. In the book, R. Kook related how, after the Six Day War, there was a meeting between government officials and roshei yeshiva. Representing the government and army was Moshe Dayan, and representing the yeshivos were R. Yechezkel Abramsky, R. Tzvi Yehudah Kook and R. Chaim Ya'akov Goldvicht. When Moshe Dayan asked why yeshiva students are exempt from the army while other youths fight and die to protect the country, R. Tzvi Yehudah Kook responded that he rejects the term "exempt". His students are not exempt from the army but delay entry for a few years to solidify their Torah education before going out to defend their country. Throughout the book, R. Kook advocates juggling these two imperatives -- Torah study and army service -- by first solidifying one's Torah accomplishments and only then serving in the army.
Cf. R. Shlomo Aviner, Am Ve-Artzo, vol. 2 pp. 523-531.