They actually did open up the PDF, believe it or not. The standard is currently controlled by ISO, and has been since 2008.
The problem is that PDF is such a shitty format that no one but Adobe really wants to bother trying to work with it. That, and Adobe still owns a lot of the patents for "shit you can do to a PDF" so everyone else has to engineer their own solutions to get around that if they don't want to pay to license.
Im just curious, what makes you say that PDF is a shitty format? I remember starting to read a book on PDFs before when I was trying to learn to code with them and being surprised how much work it actually entailed.