Do polarizability and electron delocalization have analogous effects on leaving groups? With respect to bimolecular substitution and bimolecular elimination reactions, both electron delocalization and polarizability have an analogous effect on a species, making them good leaving groups.

For example I- is a good leaving group since its negative charge is spread out over a large area.

Also, the tosylate ion is a good leaving group because of electron delocalization where its electrons are spread out over a large area due to resonance stabilization. 

However, the analogy seems to break down when considering their nucleophilicity in aprotic media, I-  is a good nucleophile and tosylate is not.

Is there a fundamental problem of the analogy between polarizability and electron delocalization?
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.