Some refiners have polymerization plants that take c4-c6 and make longer molecules. We did haul light naphthas around to ethylene crackers as well. Third place I saw them disappear was into 3rd world markets where blenders loaded them up with lead and sold it as gasoline (Nigeria, Vietnam eg).

Butanes can also be left in the refinery fuel gas streams to some extent backing out purchased nat gas.

And you are right, there isn't much you can do to lessen lifht end yield except reduce severity in your cracking units which is the wrong direction in high demand season.