And yet the vice versa would be true. Britain would not want to illegalize slavery if they owned the south because they would then lose their access to cheap cotton. Barbados on the other hand barely contributed when it came to cotton, if not at all.
I think you would need to demonstrate that abolition would translate into higher costs for the British. The American South was not the sole source of British cotton, merely the largest; large amounts of cotton were also imported from Egypt and India, where it was produced by wage-labourers or by sharecroppers. Unlike tobacco, cotton-production was heavily capital-intensive, so the cost of labour had a lower impact on the market price of crop; the primary beneficiaries of the lower cost of slave labour compared to other forms of labour were the slave-owners themselves. In our timeline, cotton prices jumped during the Civil War due to the sudden restriction of supply, but more or less normalised after Southern production resumed.
It's possible that the scenario you outline may have lead to more resistance to the abolition of slavery among the British ruling class, and the terms of abolition may have been even more generous to the slave-owners than they were historically, but I don't see any evidence that it would have fundamentally changed the circumstances leading to abolition.
Just because wealth is, theoretically, endlessly inheritable does not mean it happens in practice. If your great-great grandpa exploited my ancestor, but son of the former then left literally nothing to his son... am I still justified in asking restitution from you?
Social inequality and wealth gaps need constant management and reducing, but framing this in terms of restitution is rarely practical.
I don't disagree. My concern here is one of principle, that the moral culpability associated with the product of exploitation simply dissolves with the passage of time, or with the changing of hands. That blood money is transmuted, by nothing more than the passage of time, into simple money. It strikes me as a form of money laundering, creative accountancy replaced with patience. Stolen goods which have changed hands remain stolen goods, and the current holder has no right to deny their return to the original owner, even if those goods were received in good faith.
This is important to clarify precisely
because it allows us to detach culpability from bloodline: it's clearly unsatisfying that culpability should simply dissolve on the death of the original culprits when the wounds remain open, so we can either follow the money or we can treat it as something passed from parent to son, we can treat culpability as either
heritable or as actually
hereditary, and I'm sure you'll agree that the latter is altogether more dangerous precedent.