  Studying the physical and chemical properties of cold and dense molecular
clouds is crucial for the understanding of how stars form. Under the typical
conditions of infrared dark clouds, CO is removed from the gas phase and
trapped on to the surface of dust grains by the so-called depletion process.
This suggests that the CO depletion factor ($f_{\rm D}$) can be a useful
chemical indicator for identifying cold and dense regions (i.e., prestellar
cores). We have used the 1.3 mm continuum and C$^{18}$O(2-1) data observed at
the resolution of $\sim$5000 au in the ALMA Survey of 70 $\mu$m Dark High-mass
Clumps in Early Stages (ASHES) to construct averaged maps of $f_{\rm D}$ in
twelve clumps to characterise the earliest stages of the high-mass star
formation process. The average $f_{\rm D}$ determined for 277 of the 294 ASHES
cores follows an unexpected increase from the prestellar to the protostellar
stage. If we exclude the temperature effect due to the slight variations in the
NH$_3$ kinetic temperature among different cores, we explain this result as a
dependence primarily on the average gas density, which increases in cores where
protostellar conditions prevail. This shows that $f_{\rm D}$ determined in
high-mass star-forming regions at the core scale is insufficient to distinguish
among prestellar and protostellar conditions for the individual cores, and
should be complemented by information provided by additional tracers. However,
we confirm that the clump-averaged $f_{\rm D}$ values correlates with the
luminosity-to-mass ratio of each source, which is known to trace the evolution
of the star formation process.
