PDF metadata viewing capability is not provided on any cell phone's operating system.
There are third-party apps that may allow you to do that.
So if you've already wasted your valuable time trying to figure this out with the Acrobat Mobile App keep reading.
For any app or program to display a file's Metadata, the operating system must facilitate the user with the appropriate "Shell" [wether it be a command line interface (CLI) or a graphical user interface (GUI)] to access the device's File Viewer.
And in order for the operating system to deliver that commodity it must provide a Shell that enable any apps or programs with access to the operating system's file structure.
In addition, the operating system must not restrict the hosted programs (or apps) from accessing the desired file system directories.
Anyway, the best answer for you at this time is that no mobile operating system (that I am aware of) provides a shell that is capable enough to view PDF file metadata with the exception of more sophisticated tablet devices.
You may, however, download a third-party PDF metadata viewer that is supported by the operating system of your mobile computing device; Google Play (if on AndroidOS) or the Apple Store (if on iOS)
Make sure to test it to see how well or how bad it interfaces with the file system.
NOTE:
Please don't forget to use the links below to voice your opinion and request such an excellent feature (as you've suggested):