I'm glad you asked, since I've been pondering this for a while. $subject is my new project slogan. Now I'm not sure whether we can actually use it, because a) it's stolen from Debian, and b) another (commercial, proprietary) database product already uses the "universal database" line.
I have come to appreciate that the "universality" of a software proposition can be a killer feature. For example, Debian GNU/Linux, the "universal operating system", might not be the operating system that is the easiest to approach or use, but once you get to know it, the fact that it works well and the same way on server, desktop, and embedded ensures that you never have to worry about what operating system to use for a particular task. Or Python, it's perhaps not the most geeky nor the most enterprisy programming language, but you can use it for servers, GUIs, scripting, system administration, like few other languages. It might as well be the "universal programming language". A lot of other software is not nearly universal, which means that whenever you move into a new area, you have to learn a lot of things from scratch and cannot easily apply and extend past experiences. And often the results are then poor and expensive.
The nice thing about PostgreSQL is that you never have to worry about whether to use it, because you can be pretty sure that it will fit the job. Even if you don't care whether something is "open source" or "most advanced". But it will fit the job. The only well-known exception is embedded databases, and frankly I think we should try to address that.