As I understand it, most US refiners in the gulf region are tuned for heavier/sourer crudes than is produced domestically. I'm not entirely sure why that is (maybe a historical artifact due to prevalence of those grades in Latin America?), but the result is that we generally want to import crudes for refining.

Which is to say: the light/sweet crudes produced domestically are not the ideal feedstocks for our refiners, so restricting exports of those wouldn't necessarily increase supply of refined products.