JF:
Your question is not relevant vis-vis Chareidim. The Chareidim were there long before the Zionists foisted their disasters on our holy land against the wishes of the Chareidim, and the Zionists must leave them alone. Nothing to discuss there.
As for what the the Israeli government should do if Israelis refuse to serve, that is, indeed, a fair question and the likely answer is that, in theory, like any good government, they should govern “by the people” and therefore switch to a professional army as is done in all normal civilized countries.
The reason that neither of the above is realistic is, of course, that mandatory IDF service is an integral part of Zionist shmad, of turning its Jews into goy hebrew “Israelis”, and Zionism without shmad is simply impossible because they are both one and the same.