Why don't molecules of ionic compounds exist?
Ions are electrostatically bound.  One need only separate them with inegrated inverse squared distance work.  If you mix multiple ionic compounds in solvent, a melt, gas phase, the original paired associations are spontaneously scrambled.  Benzene plus xylene does not give you toluene.  "Separating" benzene is not electrostatic attraction.

Quaternized glycine, $\ce{^{+}N(CH3)3-CH2-C(=O)O^{-}}$, is betaine.  It is ionic, but the ions are covalently bound into a molecule.  Where are the discrete formula units in alumina?  You can draw lines to connect closest atoms, but those are not bonds. (Note fractional atom counts for atoms embedded in planes, edges, and corners.)