I don’t think we need to go to Mod’s argument. Lomed, your argument rests on a false premise. Austritt was not based on religious institutions espousing non-Torah values; indeed, the fact they are espousing non-Torah values makes then irreligious. It was based on Jewish institutions – institutions that have an obligation to adhere to the Torah. Yes, the State is an anti-Torah institution. It doesn’t need to interfere in the religious lives of its citizens. The Torah gives us guidelines of how to run a State, how to engage in war, deal with other nations, dissenting locals, and other political functions. A Jewish run political system that does not adhere to these guidelines is un-Jewish and subject to austritt.
Utilitarian balancing of the costs and benefits of the State may be appealing, but I don’t think it is correct. First, who is to say objectively what are the “good” and “bad” consequences of the State. I think God may be able to make that kind of judgement; we don’t know enough to do so. All we can do is look to the law as God gave it to us.