Sisko is all the proof you need of why the black man can't be allowed to travel through time.
But, to be fair, he was only half black man. The other half was nonlinear space ghost (but not Space Ghost.)
No, both his parents were fully human. It's just that one of them had been temporarily possessed by a Prophet in order to ensure she married his father and conceived him. So the Prophet wasn't one of Sisko's biological parents, more just his parents' matchmaker. (Or the being that enslaved his biological mother's will and forced her to mate with his father, which is actually rather disturbing.)
Well, what if the black guy (or a white guy, or a black woman etc.) went further back - say to Ancient Rome or Ancient Egypt? He could set himself up as a god, ban slavery and maybe prolong the hegemony of Rome or Egypt, changing the political map profoundly and creating a slaveless social paradigm for the developed world millennia ahead of schedule.
There goes the Western history education again, equating the West with the world. Historically, the most globally powerful and expansive civilizations on Earth have usually been in Asia. And while they had some commerce with Rome, their history certainly wouldn't have been materially affected by its policies. No empire could have really global influence until the Industrial Age.
And there's no way you could preserve civilizations for that long a time, due to all the other historical factors in play. The only reason Egypt lasted so long is because it was isolated, and even so, it got conquered repeatedly. And Rome became a victim of its own expansiveness, growing too big to govern and thus fragmenting (though its Eastern half, aka the Byzantine Empire, endured a thousand years longer than its Western half, another thing that Western-biased history educations tend to gloss over). Anyway, civilizations always rise and fall and change over time. Try instituting a change thousands of years back and you just guarantee that it'll get swallowed up by the fluctuations of history.
Not to mention that, until industrialization, it was quite difficult to manage an agrarian economy without slavery. You can't expect morality alone to govern such decisions. Slavery was prominent where there was an economic need for it. The American South didn't cling to slavery because they were more evil than the North, but because their plantation economy was dependent on slavery whereas the North's industrial economy wasn't.
And bringing about the Industrial Revolution early wouldn't work, for a variety of reasons. For one thing, it would only have happened when the right combination of need, opportunity, and social dynamics came together; otherwise any attempt to trigger it artificially would've fizzled out. (China was advanced enough to industrialize 700 years before Europe did, but they were comfortable enough that they had no need to do so. Europe's industrialization was driven by their relative lack of resources and their need to acquire and compete with the wealth of China.) For another thing, industrialization actually made slavery worse; it was the heavy demand for cotton in the textile factories of the industrialized world that increased plantations' need for slaves and drove them to work their slaves harder and more cruelly. Although in the long run, it was probably that cruelty that turned the world off of slavery and led to it being outlawed after thousands of years as a social norm. So the question is whether one would be willing to encourage a century or two of atrocity and horror in order to shock the world into banning the practice.