Based on archival {it Chandra} data, we have carried out an X-ray survey of 69, or nearly half the known population of, Milky Way globular clusters (GCs), focusing on weak X-ray sources, mainly cataclysmic variables (CVs) and coronally active binaries (ABs). Using the cumulative X-ray luminosity per unit stellar mass (i.e., X-ray emissivity) as a proxy of the source abundance, we demonstrate a paucity (lower by $41%pm27%$ on average) of weak X-ray sources in most GCs relative to the field, which is represented by the Solar neighborhood and Local Group dwarf elliptical galaxies. We also revisit the mutual correlations among the cumulative X-ray luminosity ($L_X$), cluster mass ($M$) and stellar encounter rate ($Gamma$), finding $L_{X}propto M^{0.74pm 0.13}$, $L_{X}proptoGamma^{0.67pm0.07}$ and $Gamma propto M^{1.28 pm 0.17}$. The three quantities can further be expressed as $L_{X} propto M^{0.64pm0.12} Gamma^{0.19 pm0.07}$, which indicates that the dynamical formation of CVs and ABs through stellar encounters in GCs is less dominant than previously suggested, and that the primordial formation channel has a substantial contribution. Taking these aspects together, we suggest that a large fraction of primordial, soft binaries have been disrupted in binary-single or binary-binary stellar interactions before they can otherwise evolve into X-ray-emitting close binaries, whereas the same interactions also have led to the formation of new close binaries. No significant correlations between $L_{X}/L_{K}$ and cluster properties, including dynamical age, metallicity and structural parameters, are found.
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