But ASICs that only know how to SHA256(SHA256()) could have only one plausible, and therefore illegal, use. No-one could easily compete on mining, and since building ASICs requires big factories and investment, it would be easy enough to shut down unlicensed manufacturers. Think, the Treasury would be replaced by an ASIC factory.
Illegal where? Which country's treasury? I think you're falling into the old "Bitcoin only exists within one country, and thus falls under one set of laws" fallacy.