The ⌘P shortcut is present on every Cocoa application File menu as part of the default menu bar's File menu during application development. I have never seen shortcuts simply disappear from a Cocoa applicatio's File menu in all the years I have been using OS X.
That said, yours appears to be missing, and that is a problem. Are you knowingly running any anti-virus, third-party security products, or so-called Mac cleaner applications? I saw a post yesterday in another community where a Mac was purchased from Best Buy and the store installed the Webroot anti-virus software on it. That caused sporadic keystroke issues until it was removed, but no report of missing menu items.
Paragraph 2 is important because those products can interfere with, or damage the operating system and applications. I would suggest that you attempt a Safe Boot mode process. This will clear out System caches, rebuild selected System databases (Fonts, Launch Services, etc.), and verify your boot drive. Because Safe Boot is not loading certain System kernel extensions, it will be slower to boot, and the screen may flash a few times. Perfectly normal.
Safe Boot
- Shutdown (not reboot) your Mac
- On power, press and hold the shift key until you observe the horizontal boot progress bar
- A full screen login box will appear, and in the upper right corner of the screen, you will see Safe Boot.
- After you enter your password, press and hold the shift key, and then click the right arrow to log in.
- Continue to press the shift key until your Desktop icons appear.
- Launch Pages with the same document.
Does the File menu : Print… ⌘P shortcut now appear, and work?
- Reboot normally.
- Step 6 again, to confirm shortcut is now present for the Print menu item.