1. If they are “real” Chareidim (e.g. Satmar, Neturei Karta) who hold that Torah prohibits establishing a secular nominally-Jewish state, then they are conscientious objectors. Such persons routinely minimize accepting benefits from the medinah (and refuse funding from zionist entities including the Israeli government). There are no good reasons for the medinah to conscript such persons, and probably should treat them as Arabs (i.e. Palestinian Jews) with no more rights, or disabilities that Palestinian Muslims who refuse to serve in the IDF. Such persons should be exempt regardless of whether they are learning full time or not. It should be noted that most western democracies have traditionally exempted conscientious objectors to military service, and arresting conscientious objectors would be a public relations nightmare for the medinah.
2. For individuals who accept the legality under Jewish law of the current Medinah, the only real issue the IDF’s accommodation of religious practices (or lack thereof). This could be addressed and to a certain extent is (e.g. in special units and Hesder yeshivos). For Zionists who believe that their learning is more important than playing soldier, accommodation can be done through Hesder programs or even arranging part time service or work in alternative services such as defense factories (and noting that the Israeli government considers a yeshiva student learning 20 hours a week to be full time, so many exempt students can do some gainful employment).
3. The government could tie support for yeshiva students to military service, if they similarly tied support for university students to military service, and also tied state benefits to military service. However this would alienate many non-hareidim (secular left wingers as well as Arabs) who don’t serve in the army (and according to government statistics, they outnumber hareidim who refuse military service.