Interesting question! For reference, the act itself can be read here:

http://legisworks.org/sal/2/stats/STATUTE-2-Pg426.pdf

It came into effect in 1808.

Now, there's some stuff you could say about the outcome of the law. First, even after 1808 slaves were still smuggled into the country illegally; W.E.B Du Bois wrote in The Suppression of the African Slave-trade to the United States of America, 1638-1870 that the law was nearly a ‘dead letter.’ (1) Du Bois might have been overstating that point, but he noted that much slave smuggling occurred in Florida and Louisiana, and from what I’ve read of David Ericson’s essay in Contesting Slavery,(2) once the federal government launched raids on smuggling stations in Florida and Louisiana by the early 1820s, the illicit trade all but died out.

What effects did the curtailment of the trade have? Adam Rothman’s essay, “The Domestication of the Slave Trade in the United States” in Walter Johnson’s The Chattel Principle is an excellent overview of this subject. He notes, as you do, that the U.S banned the importation of slaves at a time when there would have been great demand for them. In the Upper South, slaveowners drew a distinction between the slave trade and slaveowning; they said slaveowning was laudable but the slave trade undesirable for many reasons—Anglophobia following the American Revolution and fear that imported slaves might bring rebellious attitudes (particularly in the wake of Gabriel’s Rebellion and the Haitian Revolution) were two reasons they preferred “home-grown” slaves. People in the Deep South were more resistant to these arguments, as their economies were more reliant on imported slaves, but they eventually conceded as well. This was because they were assured that the “domestic” slave trade could handle all their needs. Remember, American slaves had an impressive natural increase! Their numbers were growing by a great deal even without importation.(3)

However, this is not to say the price of slaves wasn’t raised; indeed, the domestic slave trade became very profitable for many people in many respects. I’ll quote directly from Rothman now:

”The domestic slave trade brought economic, social, and political benefits to southern slaveowners. By selling slaves to the south and west, eastern slaveowners financed improvements to their farms, rid themselves of difficult slaves, and held the threat of sale over the heads of the rest of their slaves. By purchasing eastern slaves, southwestern slaveowners not only secured and augmented their slave labor force, but they also won the political support of eastern slaveowners who might otherwise have blocked western aspirations for the rapid settlement and development of public lands. By ripping apart settled communities of slaves and scattering the fragments across half a continent, slaveowners throughout the South immeasurably weakened American slaves’ capacity for collective resistance, which is exactly what the diffusionists had hoped would happen. In short, the emergence of the domestic slave trade, which was made possible by the prohibition on slave importation, helped consolidate a southern regional bloc committed to the preservation and expansion of slavery.” (4)

As the above passages imply, things got very nasty for the slaves—their lot certainly did not “improve.” The eminent historian Ira Berlin demonstrates this quite forcefully in chapter three of The Making of African American: The Four Great Migrations (a brief but thorough overview of African American history well suited for non-academics):

”Slaves, especially young women, found themselves subjected to all manner of sexual abuse…movement to the interior was also extraordinarily lonely and dispiriting…While women and children marched unchained, traders—worried about insurrection—shackled the men together during transit…few slaves forgot the terrifying moment when they were taken from their loved ones and sold to a distant and yet unknown place.”(5)

That last quote is a reference to the internal passage across America, not the passage from Africa to America. But your first thought might be that it refers to the latter, and that was very intentional on Berlin’s part—in his view, “[t]he similarities between the international and the internal trade could not have been lost on anyone caught in the transit to the Deep South.”(6)

It therefore seems quite fair to me to say that the well-being of slaves was lowered, not increased, by the cessation of the international slave trade. This is not, of course, to say that the abolition of the slave trade was a bad thing! It is rather to make the point that chattel slavery is miserable whether it is between continents or across them. If only they had banned slavery along with the slave trade…but as we all known, that happy day would not come until decades had passed…and much blood was shed.

Sources Cited:

1: WEB Du Bois, The Suppression of the African Slave-trade to the United States of America, 1638-1870. The whole work is available for free here:

https://play.google.com/store/books/details?id=04mJJlND1ccC&rdid=book-04mJJlND1ccC&rdot=1

I quoted from pages 109-115.

2: John Craig Hammond and Matthew Mason, eds., Contesting Slavery: The Politics of Bondage and Freedom in the New American Nation (University of Virginia Press, 2011), p. 185.

3: Adam Rothman, “The Domestication of the Slave Trade in the United States”, in Walter Johnson, ed., The Chattel Principle (Yale University Press), pp. 32-54.

4: Ibid. (same citation as above), pp. 40-41.

5: Ira Berlin, The Making of African America: The Four Great Migrations (Viking Press, 2010), pp. 99-121.

6: Ibid. 114.