Context. The apparent lack of massive O-type stars near the zero-age main sequence, or ZAMS (at ages <2 Myr), is a topic that has been widely discussed in the past 40 yr. Different explanations for the elusive detection of these young massive stars have been proposed from the observational and theoretical side, but no firm conclusions have been reached yet. Aims. We reassess this empirical result here, benefiting from the high-quality spectroscopic observations of (more than 400) Galactic O-type stars gathered by the IACOB and OWN surveys. Methods. We used effective temperatures and surface gravities resulting from a homogeneous semi-automatized IACOB-GBAT/FASTWIND spectroscopic analysis to locate our sample of stars in the Kiel and spectroscopic Hertzsprung-Russell (sHR) diagrams. We evaluated the completeness of our magnitude-limited sample of stars as well as potential observational biases affecting the compiled sample using information from the Galactic O star catalog. We discuss limitations and possible systematics of our analysis method, and compare our results with other recent studies using smaller samples of Galactic O-type stars. We mainly base our discussion on the distribution of stars in the sHR diagram in order to avoid the use of still uncertain distances to most of the stars in our sample. However, we also performed a more detailed study of the young cluster Trumpler-14 as an illustrative example of how Gaia cluster distances can help to construct the associated classical HR diagram. Results. We find that the apparent lack of massive O-type stars near the ZAMS with initial evolutionary masses in the range between ≈30 and 70 M⊙ still persist even when spectroscopic results from a large non-biased sample of stars are used. We do not find any correlation between the dearth of stars close to the ZAMS and obvious observational biases, limitations of our analysis method, and/or the use of one example spectroscopic HR diagram instead of the classical HR diagram. Finally, by investigating the effect of the efficiency of mass accretion during the formation process of massive stars, we conclude that an adjustment of the mass accretion rate towards lower values than canonically assumed might reconcile the hotter boundary of the empirical distribution of optically detected O-type stars in the spectroscopic HR diagram and the theoretical birthline for stars with masses above ≈30 M⊙. Last, we also discuss how the presence of a small sample of O2-O3.5 stars found much closer to the ZAMS than the main distribution of Galactic O-type star might be explained in the context of this scenario when the effect of nonstandard star evolution (e.g. binary interaction, mergers, and/or homogeneous evolution) is taken into account.