While it is true that Superman's race doesn't really matter, there are a few things about trying to make Superman black that need to be considered.
First of all, it is really important that Clark Kent believes that Martha and Jonathon Kent are his real, biological parents, so they would have to be black too (making them the only black farmers in all of Kansas?) I mean I guess you could try and make it so that he thinks that he was just adopted but wouldn't that just raise questions? like would the local orphanage not wonder where the hell he came from since it is a really small town? And if they just say that the Kents took in some runaway kid it would ruin the fact that they took Clark in as a baby. It is important that Superman was a newborn when he got taken in, the fact that he had a 100% earth-raised life and never even saw his home planet is kind of the driving force behind his life. And that is what so many filmakers seem to forget, that Clark Kent is the real person and Kal-El/Superman is the secret identity that he has created to be able to use his gifts to help people, but if they portrayed it as him being older than an infant when he was adopted then suddenly that gets reversed, and the character becomes kind of ruined (seriously, if you want to make a story about how an alien child lands on earth and is then raised by earthlings but is still old enough to have values/memories of his alien life to contrast with his earth life, why not just make an Icon movie? Why would you kill Superman when you have the story you want to tell right there already?)
The other thing is that Superman is just so iconic that changing a single part of his design (does no one else remember how big a deal it was when DC tried to take away his little red pants?) would be like making it so that Mickey Mouse has triangular ears, people just wouldn't like it.
Finally, as many others have mentioned, there are already 3 big name DC heroes who already sort of are the "Black Superman" Martian Manhunter (as John Jones, not J'onn J'onzz), Icon, and Steel. Sure, none of them are as iconic as Superman (who is?) but they all got considerable mention both within the comics and through DC's other media (cartoons especially).