In the Milky Way, $sim$18 Wolf-Rayet+O (WR+O) binaries are known with estimates of their stellar and orbital parameters. Whereas black hole+O (BH+O) binaries are thought to evolve from the former, only one such system is known in the Milky Way. To resolve this disparity, it was suggested that upon core collapse, the WR stars receive large kicks such that most of the binaries are disrupted. We reassess this issue, with emphasis on the uncertainty in the formation of an accretion disk around wind-accreting BHs in BH+O binaries, which is key to identifying such systems. We follow the methodology of previous work and apply an improved analytic criterion for the formation of an accretion disk around wind accreting BHs. We then use stellar 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. We find that disk formation depends sensitively on the O stars wind velocity, the 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 the assumption of a low wind velocity may lead to predicting that most of the BH+O star binaries will have an extended X-ray bright period. However, 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, producing a strong bias for detecting high mass BH binaries in X-rays with high BH spin parameters. We conclude 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 inform us about BH kicks and the conditions for high energy emission from high mass BH binaries. (Abridged)
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