Some apps do, the most used I know of is Blackmagic's Davinci Resolve, the video editor with a relatively full featured free edition available. I think this has more to do with its roots being in a high end networked environment but still, the local desktop version installs Postgres.

Oh, interesting! But that's more of a desktop application now, right? I was thinking of web servers when writing the article, but I can see how that's not totally clear. :-)