Even people who believe the administrative state is constitutional rest that conclusion on the premise that "rulemaking" is merely the formalization of the exercise of enforcement discretion. But that means that rulemaking must be performed by the executive branch, because that is the branch charged with enforcement of the law.

DMCA rulemaking is actually an example of something that would probably be constitutional if the executive did it--even if administrative agencies in general are unconstitutional. The DMCA creates civil and criminal penalties, and calls for rulemaking to define exceptions to those penalties. Defining exceptions to civil and criminal liability falls squarely within executive enforcement discretion.