  Cosmic rays regulate the dynamics and the chemical processes in the densest
and coldest regions of the ISM. Still, the determination of the cosmic-ray
ionisation rate of H$_2$ (${\zeta^{\rm ion}_{{\rm H}_2}}$) is plagued by
uncertainties in the adopted chemical networks and the analysis techniques.
This work aims to homogeneously estimate the ${\zeta^{\rm ion}_{{\rm H}_2}}$ at
parsec scales towards the Orion Molecular Clouds OMC-2 and OMC-3, probing its
variation across a whole star-forming region and a range of column densities
never explored before. The most recent ${\zeta^{\rm ion}_{{\rm H}_2}}$
estimates are based on o$-$H$_2$D$^+$, whose abundance we proxy through CO
depletion taking advantage of the existing correlation between the two
parameters. We therefore employ observations of C$^{18}$O (2$-$1), HCO$^+$
(1$-$0) and DCO$^+$ (3$-$2) towards OMC-2 and OMC-3 to determine the depletion
factor, the deuteration fraction and, ultimately, a map of ${\zeta^{\rm
ion}_{{\rm H}_2}}$ in these two regions. The depletion factors and deuteration
fractions correlate with the total column density of H$_2$, the N$_2$H$^+$
emission and the coldest fields across OMC-2 and OMC-3. The cosmic-ray
ionisation rate shows values of ${\zeta^{\rm ion}_{{\rm
H}_2}}\sim5\times10^{-18}-10^{-16}$~s$^{-1}$, in agreement with previous
o$-$H$_2$D$^+$-based estimates. In addition, it shows an overall decrease for
increasing $N(\mathrm{H_2}$), consistently with the predictions from
theoretical models. Our approach provides results comparable with theoretical
predictions and previous independent studies, confirming the robustness of the
analytical framework and the viability of CO depletion as proxy for
o$-$H$_2$D$^+$. By exploring the major limitations of the method, we suggest
interferometric observations as mandatory to reliably constrain the
${\zeta^{\rm ion}_{{\rm H}_2}}$ also at parsec scales.
