You're not factoring in lawyers. They make a big difference. It has more to do with money and less to do with race.
Now I certainly don't suggest that race is the only factor here. The USA is a very classist society, not least due to a residual Calvinism that equates earthly wealth with a sign of God's favor and thus some inherent moral superiority, a view which seems to have been implicitly incorporated into the platform of one major political party.
But the number of death sentences in Alabama isn't large. ~250 since 1980. The percentage of murders that are white on black is about 3% of all murders. And white men murder women about 30% of time they commit murder. So we are talking about probably 1-2% of all murders are white male on black female.
So you'd only expect 2-5 white people on death row in Alabama for murdering a black woman. That is way way way too small of a sample size to make bold claims on.
Though, I'm pretty damn sure racism has an impact on sentencing.
That's HUGE.
I won't venture to guess whether there are regional differences as well...
Even though it's a naive idea, I still think that everyone should be entitled to the same level of legal support in a criminal case regardless of your socio-economic status.
Explosive growth in income inequality makes the debate meaningless. There won't be grades of legal support, they'll just be billionaires who above the system and dirt poor peasants who get no support at all. Now (or recently) is probably not a good cultural era to go into the defense attorney field, for example. Being a defense attorney in an era where no one needs or can afford a defense attorney is like being a really great star trek warp field engineer in 2015, thats nice but how do you pay your bills?
If you assume the problem is racism, while in reality it's income, your earnest efforts to combat racism will be do nothing (at best) to solve it.
Legal support is a finite resource. There are only so many lawyers (thank god!) and of those that exist, some lawyers are better than others. It's simply not possible to give everyone the exact same quality of representation, short of ensuring that everyone has zero.
This is just one example of what the price system does in the market. The whole point is that resources are scarce, and the means of indicating how important a resource is for some purpose, is by voting with your money. And it's turtles all the way down: what gives you that money to indicate the importance of the scarce resource, is that you're providing some scarce resource to other people, who are paying you, and they are doing the same, and so on...