We present a detailed investigation of observable properties associated with the relative stability of the rocksalt $\mathrm{}\left(B1\mathrm{}\right)\mathrm{}$ and cesium chloride $\mathrm{}\left(B2\mathrm{}\right)\mathrm{}$ phases in the $\mathrm{AX}$ $(A=\mathrm{Li},$ Na, K, Rb, Cs; $X=\mathrm{F},$ Cl, Br, I) crystal family. Thermodynamic $B\overrightarrow{1}B2\mathrm{}$ transition pressures and $\Delta Y=Y\left(B2\mathrm{}\right)\mathrm{}-Y\left(B1\mathrm{}\right)\mathrm{}$ differences in total energies, volumes, and bulk moduli at zero and transition pressures are computed following a localized Hartree-Fock method. The arrangement of the data in clear trends is shown to be mainly dominated by the cation atomic number. This behavior is well interpreted in terms of a variety of microscopic arguments that emerge from (i) the evaluation of the energy Hessian at the $B1\mathrm{}$ and $B2\mathrm{}$ points and (ii) the decomposition of the energy and pressure in anionic and cationic classical and quantum-mechanical contributions.