A lot of angles are already covered in the comments so I'll focus on one I'm not seeing yet.

I think slavery & civil rights in the context of storytelling have some really fascinating dynamics with a lot of dramatic potential, and I think that 99.9% of moves that go for those subjects/settings shy away from exploiting that potential out of a misguided sense of respect. If more of them abandoned this attitude I doubt people would be complaining about them. But when the only tone you feel comfortable going for is 'solemn' there are only a handful of stories you can tell so even the well-made ones get repetitive.

That's part of why I enjoyed Django Unchained - it occasionally managed to stop being about the institution and start being about the characters and their insane relationships to one another. I really wish it had gone farther in that direction.

I'm trying to think of examples of 'loaded' historical settings used to their full potential - I'm sure there are better ones but the third season of Deadwood comes to mind. It could have played out as a dull cautionary tale about the evils of capitalism. (Even if they have a point do we really need another one of those?) But the creators were way more interested in using those evils as a backdrop to explore their characters. Forget about why this matters to you or to me or to the world - forget about what we can learn from this story - that's not why we're here. What we want to know is why does this institution matter to these characters? Maybe it matters to them in ways we have trouble grasping in modern times. Or maybe it doesn't matter to them at all! That kind of thing is worth exploring even if it contradicts what we think of as the 'lesson.'

TL;DR: It's not the subjects it's the attitude. Change the attitude and there are still tons of good stories to tell.