Oh they still have to leave at the end, the US' biggest mistake was believing the fairytale of peaceful melting pot coexistence as an excuse to take the easy way out half way through, instead of deporting them as even the emancipators with any political foresight argued for. Plenty of other nations and empires had way more slaves for way longer without these problems because they understood that the default outcome for a slave is not assimilation, that is the exception.

But sending them back without a disincentive against returning doesn't work either. A couple years of hard labor should stop the revolving door. Even if you want to argue bringing them over in the first place was still the US' biggest mistake, they're already here. Getting an economic boon in addition to giving a strong "and don't come back!" kick in the ass out the door is just a win/win