ABSTRACT Strong variability is a common characteristic of the prompt emission of gamma-ray bursts (GRB). This observed variability is widely attributed to an intermittency of the central engine, through formation of strong internal shocks in the GRB-emitting jet expelled by the engine. In this paper, we study numerically the propagation of hydrodynamic jets, injected periodically by a variable engine, through the envelope of a collapsed star. By post-processing the output of 3D numerical simulations, we compute the net radiative efficiency of the outflow. We find that all intermittent jets are subject to heavy baryon contamination that inhibits the emission at and above the photosphere well below detection limits. This is in contrast to continuous jets that, as shown recently, produce a highly variable gamma-ray photospheric emission with high efficiency, owing to the interaction of the jet with the stellar envelope. Our results challenge the variable engine model for hydrodynamic jets, and may impose constraints on the duty cycle of GRB engines. If such systems exist in nature, they are not expected to produce bright gamma-ray emission, but should appear as X-ray, optical, and radio transients that resemble a delayed GRB afterglow signal.