I thought this sounded outrageous, but then it occurred to me: when was the last time anyone ever used telegrams? There can't be many uses of them - I've never used one in my entire life - and all the regular costs of a business still need to be paid and the couriers have to be paid and so on.
There exist a variety of circumstances where a business has to put a piece of paper in someone's hand within about 24 hours. It's doable between virtually any two endpoints in the first world. It also costs whatever FedEx/DHL/etc think they can get out of a business which needs to have a document hand delivered on the other side of the world immediately, which is "a lot." (e.g. It's presently midnight on Wednesday in NYC. I can walk next door to a store in Tokyo and hand FedEx a letter. It will arrive at the New York Stock Exchange before the opening bell on Thursday. That will cost ~$125 but it will almost certainly actually work.)
Some 60-70 years ago, you could not get it done for any sum of money. Maybe the military could do it, on a good day. A few years later, it's not just possible, but cheap.
I also didn't bother to check Fedex/DHL because I figured while they probably did have faster deliveries than USPS, they always charge way more and we were unsure we really needed within a day delivery (which is the only place on the Pareto frontier the private companies would be for general document delivery).
As it happened, we were unsatisfied with our options so we kept digging and eventually came up with what we think are the phone number & email address of the person we need to reach, so hopefully it all turned out to be moot.