It is possible that the states with higher murder rates keep the death penalty because people are concerned about their high murder rates and so support the death penalty in the belief that, without it, the murder rates would be even higher. In other words, higher murder rates may be the cause of the death penalty, not vice versa.

Having lived in Louisiana, I think that might be a realistic interpretation in that case.

For what it is worth, I oppose the death penalty not on principle but because in practice, in this country, it is always imposed with race and class bias.