Stripped-envelope supernovae (Types IIb, Ib, and Ic) that show little or no hydrogen comprise roughly one-third of the observed explosions of massive stars. Their origin and the evolution of their progenitors are not yet fully understood. Very massive single stars stripped by their own winds (≳25−30  M _⊙ at solar metallicity) are considered viable progenitors of these events. However, recent 1D core-collapse simulations show that some massive stars may collapse directly into black holes after a failed explosion, with a weak or no visible transient. In this Letter, we estimate the effect of direct collapse into a black hole on the rates of stripped-envelope supernovae that arise from single stars. For this, we compute single-star MESA models at solar metallicity and map their final state to their core-collapse outcome following prescriptions commonly used in population synthesis. According to our models, no single stars that have lost their entire hydrogen-rich envelope are able to explode, and only a fraction of progenitors left with a thin hydrogen envelope do (IIb progenitor candidates), unless we use a prescription that takes the effect of turbulence into account or invoke increased wind mass-loss rates. This result increases the existing tension between the single-star paradigm to explain most stripped-envelope supernovae and their observed rates and properties. At face value, our results point toward an even higher contribution of binary progenitors to stripped-envelope supernovae. Alternatively, they may suggest inconsistencies in the common practice of mapping different stellar models to core-collapse outcomes and/or higher overall mass loss in massive stars.