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Expressing system specifications using Computation Tree Logic (CTL) formulas, formalising programs using Kripke structures, and then model checking the system is an established workflow in program verification and has wide applications in AI. In this paper, we consider the task of model enumeration, which asks for a uniform stream of output systems that satisfy the given specification. We show that, given a CTL formula and a system (potentially falsified by the formula), enumerating satisfying submodels is always hard for CTL--regardless of which subset of CTL-operators is considered. As a silver lining on the horizon, we present fragments via restrictions on the allowed Boolean functions that still allow for fast enumeration.