Why does delocalization (only) occur in molecules represented by resonance hybrids?
A short answer is that we mostly use resonance structures to represent delocalization when the bond orders or formal charges predicted by VBT are not approximately integers, simply because non-integer bond orders and charges are more cumbersome to draw. A typical example is a carboxylate, which we could draw with 1.5 bonds between both C-O pairs and -0.5 charge on each O, but it is simpler to just draw a resonance structure with one C=O double bond and one C-O single bond and a full -1 charge on one oxygen.
As others have noted, electrons are still delocalized across the entire molecule in molecules for which we do not use resonance structures. The difference is that we can approximate the bond orders in those cases as integers, so only one structure is needed to represent that.