Do polarizability and electron delocalization have analogous effects on leaving groups?
TL;DR: Nucleophilicity is primarily a kinetic phenomena.  Leaving group ability is a thermodynamic phenomena.

The stabilization of an anion by delocalization of charge means that the resulting products will have lower energies than alternate situations. In accordance with the Hammond postulate (a few logical steps skipped), transition state barriers with low energy products will be smaller than those with higher energy products.

However, for a bimolecular reaction to occur, the molecule must have 'proper collision speed and orientation'.  Diffuse charges (over multiple atoms) generally make this more difficult.  This extra facet of the of the geometry of the transition state is why the equivalent stability argument does not apply to both leaving group ability and nucleophilicity.