Both of you are assuming random IDs protect user privacy. The only thing I can come up with where that to be true (without things that no one was ever seriously suggesting or using, such as a sequential identifier that increments on something per user) is that someone who is unable to see a resource otherwise will know when it was created (and in fact the time when something was created is now information about a thing "at all" when it otherwise might not have been). What am I missing?

Otherwise, the arguments against sequential identifiers seem to mostly come down to either people who somehow dislike scraping (which I might even argue is immoral, and I think this great comment from dredmorbiu come at it from the correct mentality; hell, I strongly prefer it--as a potential user--when a site is scrapable) or people who don't want anyone to know "true truths" about their service, with examples such as "our user growth figures" (but these help the site operator, not the users).

(I am also surprised to see Parlor brought up even in this great comment about "you didn't really stop me from figuring out what I wanted to know": to the extent to which you want to do "defense in depth"--which I honestly find frustrating as an argument by itself, as you can use that to justify almost anything, including absolutely ridiculous things we tend to claim are "security by obscurity"--you are going to then need to make sure you really really lean into the idea that "we wanted our site to not be scrapable, even to an administrator", which I can't imagine anyone ever actually doing for myriad reasons including how sites usually help search engines.)