There's quite a bit to unpack in this question, so I'm going to try and give you a straight-forward answer without going too much off your core topic if I can. Please do let me know if you want me to elaborate on anything.

You're right that America was unique for its role in the trasatlantic slave trade, but for the wrong reasons - America is unique because by the time of its independence it does not need the slave trade to sustain African slavery. Whilst Americans absolutely participated in the slave trade a slavers, traders, buyers and financiers, the United States was not the main destination of the slave trade, which was overwhelmingly a European enterprise. Between the 1620s and 1860, an estimated 472,000 African men, women and children were transported to continental North America. That pales in comparison to the very nearly 6million people who went to European colonies in the Caribbean and the Guianas, or the 5.5million who arrived in Brazil, where slavery persisted legally for more than two decades after the end of the US Civil War. Whilst some of the nearly 3million people who were initially transported to the British Caribbean did find themselves ending up in the United States, particularly in the colonial period, the US was not as you perhaps imagine it the ultimate destination of the vast majority of slave ships.

Slavery had been a feature of life in the colonies that would become the United States since the earliest days of sustained European colonisation. In the mid-17th century, the British begin to take African people in their thousands from the coast of West Africa to North America and the Caribbean to be used as slave labour; between 1640 and 1680 we see the British bring around 200,000 people to the New World from the West Coast of Africa, and that figure more than doubles between 1680 and 1720, and it then very nearly triples between 1720 and the American revolution in 1776. So when the United States becomes an independent nation, it is not suddenly deciding to get involved in the transatlantic slave trade whilst an increasingly enlightened Europe looks on in horror; more than 40,000 African people a year were being taken from the coast of western Africa to the New World by the time the future United States declared their independence from Britain, and the British, French, Portugese and Dutch were all involved in sophisticated slave trade operations. So there's nothing uniquely American about the practice of taking captives from Africa to the New World; this is a European enterprise that America is involved with precisely because the United States began their lives as European colonies. Indeed, you get individuals like Thomas Jefferson who try to rationalise the existence of slavery in the United States as an evil forced upon them by the British Empire, and blame Britain for the fact they now have to wrestle with the problem of being a slave society that claims to value freedom and self-determination so profoundly.

So if the United States in the post-independence era was not the driving destination of the slave trade, then why is the United States so central to the story of transatlantic slavery? The answer to that lies in the fact that the system of slavery in the United States was unique in the New World for being able to thrive without the arrival of new captives from West Africa. In large parts of the Caribbean, the predominant crop slave labour was used to grow and harvest was sugar, and sugar is a particularly labour-intense crop. As a consequence, the African Caribbean death rate on British sugar estates in places like Jamaica and Barbados was on average probably about twice as high as the African American death rate on plantations and small farms in Virginia for all manner of reasons (more intense labour not only means greater risk of injury or death through work, but also less time to care for children, greater susceptibility to disease and so on). Enslaved Africans everywhere in the New World tried earnestly to live lives that were as vibrant and as rich as they possibly could, and that included having strong and dynamic family lives wherever possible. In the sugar colonies of the Caribbean and Brazil though, higher mortality meant that African Caribbean slaves did not have enough children surviving to adolescence to overcome the higher death rate, leading to consistent population declines for most of the period. In contrast, lower mortality rates in the United States mean that enslaved populations do grow consistently and organically.

As a result, by the time of independence the United States is not dependent on bringing new captives over from Africa each year to ensure the continued growth of the slave labour force and the sustainability of slavery as an institution. When the revolutionary war for independence breaks out against Britain, we actually see the governments of the various states take action to outlaw or suspend the slave trade as part of a strategy of economically undermining the British Empire, and the British slave trade suffers quite seriously for it for a while. In 1775 about 46,000 African slaves arrived in the New World on a ship flying a British flag - within four years that number falls to less than 8,000. Because of that lack of dependency, although the US Constitution guarantees the protection of the slave trade in federal law for 20 years after independence, individual states largely retain the prohibition on the trade. Although it does have periods where it reopens, it doesn't really return to pre-war levels until about 1804, as the deadline at which federal abolition becomes possible looms. What really makes the United States unique in the history of the slave trade is that it develops its own enormously vibrant internal slave trade, with African Americans being sold within and across state borders (there is an intra-Caribbean trade as well, but it functions as an extension of the transatlantic trade). Both the United States and Britain permanently outlaw the slave trade in 1807, though not collaboratively; other states actually take longer to do so, and the attempt to ensure the effective enforcement of the totality of those bans by European powers doesn't really get underway in earnest until the 1840s.

So America really has a very different and unique relationship with the transatlantic slave trade; even though slavery as an institution thrives there, the particular circumstances of the North American continent mean that the slave trade from West Africa never really thrives in the same way that it does in the Caribbean and Brazil. The rights and dignity criticism tends to go in the opposite direction, with even some American slaveholders attacking the transatlantic trade as barbaric and inhumane (though not without ulterior motive - the re-opening of the transatlantic trade would, of course, reintroduce competition for the rapidly growing and thriving internal trade!), and those criticisms extended to other places where slavery existed as well, especially British sugar colonies. Particularly in the 19th century southern US, slave owners worked hard to develop an ideological and philosophical system that would justify slavery not as a necessary evil, but as a morally just and righteous institution. Pro-slavery ideologues would frequently use the sugar plantations of the Caribbean as an example of a particularly heinous and unpleasant form of slavery, and contrast it with what they tried to frame as their generous-spirited, uplifting brand of slavery. Slavery in the Caribbean was posited as an exploitative and murderous institution, in contrast to the paternalistic and uplifting practice they tried to represent themselves as engaging in. The reality, of course, is that American slavery was also an intensely violent and dehumanising institution, and far from 'benign' - American slave owners tried to make similar arguments that slavery was a condition preferable to wage labour in the North and parts of industrialised Europe.

Certainly there were British and European politicians and establishment thinkers who criticised America's involvement in slavery and the slave trade, but those arguments have much more to do with political rhetoric - highlighting the contradictions of American political economy and moral philosophy - than humanitarian concern. It's only really from the 1830s onwards, after the abolition of slavery by Britain in its Caribbean colonies, that the issue of slavery in the United States begins to be meaningfully taken up on a significant scale in British political debate and discourse (although the British and American abolitionist movements themselves had been developing links and influencing each other long before then). Even then, despite its sincere interest in promoting opposition to slavery in the US, the British abolitionist movement post-1838 is still first and foremost concerned with enforcing the abolition of the slave trade itself and achieving improved conditions for African Caribbean people in the colonies, whilst Britain as a nation and polity continued to readily import slave-produced goods from the US, particularly cotton for its northern textile industries. There was also backlash from some elements of society, both among the elite and the general public, who were concerned that lobbying for action against American slavery was a way to give the government an excuse to not pursue social reforms at home by focusing on a greater evil abroad (similar critiques were made of efforts to improve conditions in Britain's own colonies). In debates over tackling continued slave trading in the 1840s and 1850s, we also see reluctance on the part of the British government to inconvenience or insult the United States who, despite having outlawed the transatlantic trade at the same time as Britain, took less interest in its active prosecution abroad and had concerns about the security of ships sailing under the American flag.