PDF provided more fidelity for printing, had better tooling (it was by Adobe after all), it was cross-platform, could be displayed on the desktop, so it won. The reader was cross-platform so end-users didn't have to mess with installing plugins for various image types. And because everyone in the document creation division(1) used Postscript to print, printing to PDF was super-easy. And at some point everyone had a postscript printer driver on their machine, so printing to PDF because super-easy as well.
It's not an archiving tool, but people use it for archiving...just like the way a spreadsheet isn't a project management tool, but millions of people use it for project management.
At this point the network effects for the PDF file format would make it difficult to replace. With PDF you can practically guarantee(2) that the file will look the same on any device.
(1) This was more true back then than today, probably (2) assuming that you embedded the fonts, and that the reader doesn't suck.
What's funny is I don't think Adobe really makes any money off of PDF; it's an accidental de-facto standard.