I cannot answer for any other posters but for myself my interest in a Confederate victory in the ACW is three fold.
1) I do not agree with your implication that a CSA victory is unlikely, nor is a Confederate victory necessary for Confederate independence. There are in fact a great many Confederate independence scenarios some are very unlikely to the point they stretch the reader's credibility (e.g. some of the various steam punk offerings) other such as a Union conflict with Britain or a major Union reversal before the 1864 Union elections are far from improbable. A war over Trent for example was more likely than not right up until St Stephen's day 1862. So my first reason for liking the Confederate independence scenario is that there are so many different credible PODs to explore and they can lead to a wide variety of different time-lines.
It is certainly possible to write credible CSA victory timelines, but most attempts are not particularly credible. Looking at your examples, a Union conflict with Britain is improbable without very uncharacteristic levels of diplomatic incompetence on both sides. A major Union reversal before the 1864 elections is possible, but the most probable result of that is the Confederacy falling a couple months later, not their achieving independence.
2) My second reason for liking the Confederate independence scenario is that it is a major change in history compared with OTL. The USA can never be the superpower that it is in OTL 20th Century (unless of course it re-unites with the CSA in someway very quickly).
The US still could become a superpower, but it is less likely and would take longer than in OTL.
In all probability it will break-up because it will have lost the major source of its prosperity (the south).
The Confederacy was the major source of US exports, but that was only about 5% of the US economy. The Union still had most of its previous agriculture and infrastructure, as well as virtually all of its previous industry, mineral wealth, and shipping. US breakup after spending that much blood and treasure trying to maintain the Union is about as likely as the US Revolutionaries voluntarily rejoining the British Empire.
The CSA on the other hand is likely to be very rich in many scenarios and dirt poor in a few.
The Confederacy ended the war with $2.7 billion in public debt, over half of which was redeemable at 8% interest 6 months after the end of the war. Ten percent of the Confederacy's draft age white men were serving in the Union Army, and others were in armed rebellion against the Confederacy. Fifteen to twenty percent of adult male slaves had also joined the Union army, and many others had run away. Major portions of the rest of their work force were dead or crippled, and few immigrants would replace them. The Confederate infrastructure was collapsing due to overuse and being forced to operate at a loss by the Confederate government. Runaway inflation had destroyed much of the Confederate economy. Confederate industry would face an influx of cheaper foreign goods once the Union blockade ends, and vastly less contracts from the post-war peace-time Confederate government.
That's a notably worse financial situation than in OTL. The collapse of the Confederacy insured they would never have to pay that massive public debt, that most of the former slaves and Unionists would stay as part of the work force, that southern industry received greater levels of protection, that they had a stronger and more stable currency, and that carpetbaggers would invest in restoring and improving southern infrastructure. Rather than rich, let alone very rich, the Confederacy will probably be poorer than OTL's postbellum south.
It is possible that the CSA might become a backwater reviled by nearly every other nation but this is unlikely because in most scenarios it will be very rich and everyone will want its goods. Thus it is more probable that the CSA will become a rapidly developing, rich, major nation that practices slavery.
Odds of the Confederacy becoming a rapidly developing or a rich or major nation are all low. Achieving any of those is going to require the Confederacy overcoming the handicaps of the slave economic system, poor infrastructure, active opposition to funding internal improvements, active support of tariff levels insufficient to sustain the central government, runaway inflation, massive public debt, massive losses in the work force, and cultural disdain of immigrants. Best case, the Confederacy might become a regional power whose wealth is mostly in the hands of a small upper class.
If that is the case then I can easily see 'scientific' slavery and the combination of the worse excesses of early 20th Century ultra-Capitalism and slavery leading to monsterous slave management programmes. The CSA may possibly roll back ideas about race and slavery to pre-Wilberforce values across large parts of the globe.
While the Confederacy would probably try to bring the "benefits" of slavery to Mexico, Central America, and the Caribbean, their track record on seizing and holding hostile territory was one of unremitting and often catastrophic failure.
An independent CSA can give rise to some truely horrific dystopias than are worth exploring for the light they shed on our current societies.
The slaveholding culture of the Deep South was already developing into a dystopian culture before the Civil War - some free blacks were re-enslaved, the enslavement of poor whites was advocated, travel papers were required in many areas, assault was an acceptable method of dealing with political opposition. During the war, the Confederate government had an official policy of executing or enslaving some enemy POWs, tolerated if not encouraged violent oppression of dissenting views, and had an unofficial policy of enslaving some enemy civilians. The Confederate government voted money for saboteurs to burn down Union hotels while people slept, burn down Union theaters during performances, and attempts at germ warfare.