May I ask anyone more knowledgeable than myself why this approach - ie payment of compensation - was not considered in the US at the time?
Because abolition (with or without compensation) didn't have sufficient backing in the US to be a serious policy option until after the Confederacy made it viable by pulling most of the slave states into rebellion.
While the new Republican Party was largely ideologically abolitionist, they could only compete effectively by running on a platform of explicitly deferring abolition in the interest of preserving the Union. The current policy debate was over things like whether and under what conditions to allow expansion of slavery into new territories and states, not abolishing it where it already existed. The South expected that falling short of their preferences on this would eventually lead to abolition on some terms, of course, which led to the rebellion to prevent that from ever being an issue.
British slaves almost all lived in the colonies not in Britain itself. Freeing all the British slaves caused huge changes in the colonies but it didn't change things at home that much. Freeing all the slaves in the US is a much different ballgame because those former slaves are now citizens living right next door to you. The Southern States feared what would happen if the slaves they had been abusing for generations were freed and were given political power. In some southern states like Mississippi (if memory serves) the number of slaves was greater than the non slave population.
That's just one of many big practical reasons, there are many more, but it also can't go unmentioned that the US had built up a racist cult around slavery by this time. It wasn't just that the economic system of the south was intrinsically linked with Slavery, it was that the culture was built around the degradation of an entire race of people. They didn't keep slaves just because of money, but because they honestly believed that subjugating them was "for their own good". You can't buy someone out of a belief like that.
This is rigorously documented by the way. They believed they were morally right and didn't shy away from writing it down. All the declarations of Secession by the Confederate states contain similar language but the Texas one is particularly direct on this point:
"We hold as undeniable truths that the governments of the various States, and of the confederacy itself, were established exclusively by the white race, for themselves and their posterity; that the African race had no agency in their establishment; that they were rightfully held and regarded as an inferior and dependent race, and in that condition only could their existence in this country be rendered beneficial or tolerable." https://www.tsl.texas.gov/ref/abouttx/secession/2feb1861.htm...
The sad part is not much has changed. Those states are still full of people who fear melanin.
There is a difference, obviously the slave states saw the direction things were going, but to the question at hand it’s a material distinction.
France agreed to sever ties with its colonial possession but at an extraordinary cost to the Haitians who would remit payments for the next 125 years. This was only possible because Haiti was a country with its own resources.
Contrast that with the American South; the slaves had nothing to offer to reimburse their owners.
Sometimes I feel the removal of TR's statue was an overreaction, and then you recall this shit, and it gives pause.
For some number of years, even the discussion of slavery bans was prohibited in US Congress.