In my experience there are two types of private schools in the South (not just in Alabama). Private schools that have been around a long time that excel in academics and athletics; these schools are for the more wealthy who can write a check anytime to support the school and its programs. The other is the private school that was formed in opposition to integration in the late 1960s and early 1970s. I am not saying this is right or wrong, but it was to avoid having their children attend schools with blacks. These schools, in most cases, are not funded by the wealthy, but by ordinary people who work for a living and in some cases have to borrow to afford their children's education. That is their choice. These schools are usually small, all white and do not have the resources to compete against any schools other than those that are just like them, as it should be.
The wealthy private schools in order to compete statewide rely on their financial resources (parents) to recruit, in most cases, black athletes, which certainly gives them a competitive advantage over most public schools in their classification. This has been going on now for 50+ years and it should come as no surprise to anyone. I do believe being able to give financial aid in the form of scholarships to attract better athletes is an unfair advantage. Since my children are grown I have no dog in this fight, but it is like everything else in life, it pits the haves vs the have nots.