>I think in most places if there's a war, the losing side doesn't get that kind of treatment.
They would if the winning side actually wanted the losing side to participate in the greater country as a whole, as the Union wanted after the war. You could completely crush the losing side and destroy all of their history, symbols, heroes, and values and anything that connects them together (which we have been seeing in today's times) but Lincoln and the Union leaders did not want resentment and spite from either side lead to the complete dissolution of the country. A state cannot be successful if half it's population is forced against it's will to participate. That's why the Union declared that Confederate veterans would be treated the same as Union veterans and given proper honor and burial. It did work out quite well, because there was not another civil war US is still standing so far. Most civil wars ended with either another conflict not too long after, or a complete rewriting of the previous system.
As for the question of Southern Characteristics, have you asked people who are really from the South that? I think people too often rely on what others say of Southern characteristics. I cannot speak for them, but I have been told they value Jesus, freedom of speech and firearms, being friendly and giving, enjoying nature and the land they live on, and honest work. I think it's not often put into words because these values are so inherent that they don't often realize those values are unique until they go outside the south. Even as an outsider it can be difficult to quantify, but visiting there I can certainly sense subtle but very distinct differences in how people interact with each other and live their day-to-day lives.
Southerner here. In my opinion the reason that "it worked out quite well" is that the Union caved and ended Reconstruction in 1877. This was followed by the "Redemption" period in which Jim Crow was set into place and white supremacy was entrenched. For Southerners, both white and black, things were in many ways similar to pre-1861. White people had relatively little to complain about, and black people who shook up the status quo were subject to reprisals up to and including murder.
Meanwhile, my impression is that one thing valued in the contemporary South is "pleasantness". This showed up, for example, in the myth that slaves were happy. Today, conversation tends to be more indirect. For example, if you want to tell somebody that they're an idiot, "Bless your heart" will do the trick.
That said, despite having grown up here I never really identified with the culture, so I can't really answer the question all that reliably.
I had been sceptical about the Iraq adventure in part because my observations tell me the US attempted nation-building, in its own back yard, in 1866 and still hadn't fully managed it by 1966[1].
Looking for mid-nineteenth century civil wars, I find
https://en.wikipedia.org/wiki/Revolutions_of_1848 and maybe I'm just too ignorant of domestic politics in these countries, but it doesn't seem that any of them still have divisions rooted in those conflicts, or even still had in the mid-twentieth century.
It's unclear how much geographic sectarian division there is in the current US. I would hope most yankees would agree that Sherman was an arsonist, and most southerners would agree that lynching is despicable (and most memes I run across on the internet to the contrary of either originate in a relatively small community of trolls?).
As to the original question, try a web search on "you know you're a southerner when". There are definitely cultural differences which can be, and usually are, celebrated without any reference to the Lost Cause.
(In some ways, southern culture may be more familiar to europeans. A german[2] colleague of mine once asked me "how do you confuse an american?". "How?", I replied. "Answer them, when they ask you how you're doing.")
They would if the winning side actually wanted the losing side to participate in the greater country as a whole, as the Union wanted after the war. You could completely crush the losing side and destroy all of their history, symbols, heroes, and values and anything that connects them together (which we have been seeing in today's times) but Lincoln and the Union leaders did not want resentment and spite from either side lead to the complete dissolution of the country. A state cannot be successful if half it's population is forced against it's will to participate. That's why the Union declared that Confederate veterans would be treated the same as Union veterans and given proper honor and burial. It did work out quite well, because there was not another civil war US is still standing so far. Most civil wars ended with either another conflict not too long after, or a complete rewriting of the previous system.
As for the question of Southern Characteristics, have you asked people who are really from the South that? I think people too often rely on what others say of Southern characteristics. I cannot speak for them, but I have been told they value Jesus, freedom of speech and firearms, being friendly and giving, enjoying nature and the land they live on, and honest work. I think it's not often put into words because these values are so inherent that they don't often realize those values are unique until they go outside the south. Even as an outsider it can be difficult to quantify, but visiting there I can certainly sense subtle but very distinct differences in how people interact with each other and live their day-to-day lives.