The “made with carbon” line was ridiculous enough (aren’t all plastics made with carbon?) that I called up the Black Card people to ask exactly what material the card was made of. (Also, I’m bored at work.) The woman who took the call had to put me on hold to ask her supervisor, but eventually I was told that it’s made of carbon graphite. (FYI, the American Express Centurion card is anodized titanium, according to Wikipedia.)
It’ll give you the world! Except that it doesn’t have a chip, so there’s a good chance it won’t work in unattended card readers overseas. Oops.
If you look at the fine print on the website, it says that the card is issued by Barclay’s Bank of Delaware.
The Shocking Secret is that the Centurion concierge service is exactly the same service you get with a hoi polloi platinum card. (Of course, it seems like it’s much better, because if you have a black card you’re probably buying much more expensive stuff and services to begin with. But it’s the same people arranging all of it.)
I’ve used the concierge service for my platinum card on several occasions to organize travel and get tickets to stuff, and have been pretty pleased with them. But if I ever start earning ten times as much money, I’m not gonna waste it on a black card membership. 
If you make the money needed, you wouldn’t bat an eye at the cost. Again, the perks of having the card outweigh the fee.
Amex doesn’t even offer the Centurion card unless you charge at least $250,000 each year. So few of the patrons are going to have a problem with a $2,500 annual fee.
I’m going to go ahead and disagree with you there, unless your Platinum concierge will find and buy the horse ridden by Kevin Costner in Dances with Wolves and send it to Europe, courier you a handful of sand from the Dead Sea for your kid’s school project, or arrange for you to audition for your favorite soap opera.
They’ll do it if you’re willing to pay for it. You don’t get horses and Dead Sea sand for free, you know.
ETA: The Centurion card does come with much in the way of travel benefits and all sorts of automatic upgrades and stuff. I was only speaking of the concierge service which is the same.