I would argue that it does make it central. The fact that you can have entire adventures avoiding it doesn't mean it isn't. The same is true of literally any setting that centers a certain idea. You can run a Planescape adventure where no-one uses a portal or talks philosophy. You can run a Ravenloft adventure that doesn't involve the Mists and isn't very scary (I think that's most Ravenloft adventures actually). And so on.
But as soon as you go to any major town or encounter a big caravan or the like, slavery is going to be everywhere. The DM and players may not want to engage with it, but the setting seems pretty clear about it. The issue with slavery in particular is that the US is still recovering from that fact that barely 150 years ago they had chattel slavery (the worst form of slavery) in full force (not as something half-forgotten or decaying). And slavery in DS tends towards being chattel slavery (certainly Muls make it clear it is). So turning it into entertainment, which is what this does, effectively, without being disrespectful/weird, requires a level of engagement with the consequences of slavery that is probably not something Dark Sun really wants to engage with.
To put it another way - using it as a cheap background element that's constant and never actually looking at it in a serious way is a problem. Maybe it won't be a problem in another 50-150 years. Maybe it feels like way less of a problem in countries which weren't engaging in chattel slavery 150-odd years ago.
And I don't think it's really necessary to make it focused.
Personally I think Dark Sun needs a serious re-working, from the ground up, and I say that as a huge DS fan. Keep the basic concepts and visual style, but take an "anything can go" attitude to specifics beyond the concepts.
Yes absolutely. It's post-post apocalypse. Not peri-apocalypse or immediate post-apocalypse. I don't think it's even an argument that environmentalism is a theme. It definitely is. It's about as subtle as a brick to the face!

It's part of why DS is even more relevant now. Especially with cryptocurrency and NFTs and so on, which whilst not yet primary contributors to climate change, use more and more energy every year on pointless idiocy (and seem likely to grow exponentially), which feels very akin to Defiling.
Who is saying that though? I haven't watched the full panel, do they say it there? No-one in this thread has said anything like that.
What I am saying, for example, is that if you're going to make chattel slavery a major theme of your setting, one that's nigh-ever-present (in the City-States at least), you either need to really engage hard with the horrors of that (not really suitable for a WotC D&D setting imo), or y'know, not do it, which means having it not be a major theme.
That doesn't mean you can't have chattel slavery, let alone other forms of slavery, in your setting, but they should probably not be ever-present nor key to entire races existing. Look at other historical forms of oppression and slavery - particularly indentured servitude and use those as your main forms, and probably have City-States that don't use slavery but are horrifically oppressive anyway.
All those games massively downplay slavery and oppression, note. In Odyssey, which is the one I've played most, it's barely even a thing to a highly-unrealistic degree (just about everything about the people in the game is unrealistic, which is fine).
AC actually did have a spin-off game, possibly two, that engaged pretty hard with slavery (I forget the names, it was around the time AC Black Flag was the main game), and which were actually I thought fairly well-regarded for their treatment of it (I could be misremembering).