Refining light crude is essentially the same process as heavy crude with fewer steps. US refineries are designed to handle virtually any kind of crude and are highly configurable. That flexibility is part of what makes their refinery business so successful. US refinery capacity is ~50% larger than their domestic oil production; it is a major export business for the US.

The real cost to not processing heavy crude oil is that many refinery assets will be sitting idle because they aren't needed to process light crude.