A suite of 432 collisionless simulations of bound pairs of spiral galaxies with mass ratios 1:1 and 3:1, and global properties consistent with the ΛCDM paradigm, is used to test the conjecture that major mergers fuel the dual AGN (DAGN) of the local volume. Our analysis was based on the premise that the essential aspects of this scenario can be captured by replacing the physics of the central black holes with restrictions on their relative separation in phase space. We introduce several estimates of the DAGN fraction and infer predictions for the activity levels and resolution limits usually involved in surveys of these systems, assessing their dependence on the parameters controlling the length of both mergers and nuclear activity. Given a set of constraints, we find that the values adopted for some of the latter factors often condition the outcomes from individual experiments. Still, the results do not, in general, reveal very tight correlations, the clearest effect being the tendency of the frequencies normalized to the merger time to anticorrelate with the orbital circularity. In agreement with other theoretical studies, our simulations predict intrinsic DAGN abundances that range from ∼ a few to 15% depending on the maximum level of nuclear activity achieved, the higher the bolometric luminosity, the lower the fraction. At the same time, we show that these probabilities are reduced by about an order of magnitude when they are filtered with the typical constraints applied by observational studies of the DAGN fraction at low redshift. Seen as a whole, our results prove that consideration of the most common limitations involved in the detection of close active pairs at optical wavelengths is sufficient alone to reconcile the intrinsic frequencies envisaged in a hierarchical universe with the small fractions of double-peaked narrow-line systems which are often reported at kpc-scales.