Context. In the Milky Way, ∼18 Wolf-Rayet+O star (WR+O) binaries are known with estimates of their stellar and orbital parameters. Whereas black hole+O star (BH+O) binaries are thought to evolve from WR+O binaries, only one such system is known in the Milky Way. To resolve this disparity, it was suggested recently that upon core collapse, the WR stars receive large kicks such that most of the binaries are disrupted. Aims. We reassess this issue, with a particular emphasis on the uncertainty in predicting the X-ray emission from wind-accreting BHs in BH+O binaries, which is key to identifying such systems. Methods. BH+O systems are thought to be X-ray bright only when an accretion disk forms around the BHs. We followed the methodology of previous work and applied an improved analytic criterion for the formation of an accretion disk around wind accreting BHs. We then used stellar evolutionary models to predict the properties of the BH+O binaries which are expected to descend from the observed WR+O binaries if the WR stars would form BHs without a natal kick. Results. We find that disk formation sensitively depends on the O stars’ wind velocity, the amount of specific angular momentum carried by the wind, the efficiency of angular momentum accretion by the BH, and the spin of the BH. We show that whereas the assumption of a low wind velocity may lead to the prediction that most of the BH+O star binaries will have an extended X-ray bright period, this is not the case when typical wind velocities of O stars are considered. We find that a high spin of the BH can boost the duration of the X-ray active phase as well as the X-ray brightness during this phase. This produces a strong bias for detecting high mass BH binaries in X-rays with high BH spin parameters. Conclusions. We find that large BH formation kicks are not required to understand the sparsity of X-ray bright BH+O stars in the Milky Way. Probing for a population of X-ray silent BH+O systems with alternative methods can likely inform us about BH kicks and the necessary conditions for high energy emission from high mass BH binaries.