Why does Ubuntu not ship with a way to fill in PDF forms?
As of "Evince" version 3.10.3 (that is Ubuntu 14.04) it is possible to do this with "Evince" and that is installed in a default install. It is called "document viewer" if you want to search for it. "evince" to start from command line.
From gnome.org on filling forms:
Forms
When filling out an interactive form, you can navigate from field to field by clicking on a field with your mouse. When you are finished filling out a text field, press Enter.
You can make a selection in a scrollable list box by clicking on the list box and scrolling to your choice with your mouse.
Regarding the question:
Why does Ubuntu not ship with a way to fill in PDF forms?
It does as shown above but in general software might not be included due to legal reasons. Software that can open and manipulate a PDF that has some sort of restriction in it would cause a legal problem for the maintainer of that operating system: it would require paying a fee for allowing to circumvent it (same as with audio and video codecs: those are not shipped with Ubuntu but can be added afterwards).
Most likely because there's not an open-source implementation of the entire "new" PDF forms specification, called XFA. Older forms (FDF) are generally supported.
While XFA is technically an open standard, like Office Open XML, it is basically a giant glop of a file format that Adobe "documented" to meet government requirements for open file formats. The current version of the specification (3.3) is 1584 pages long (just for the forms feature, not all the rest of PDF) and includes such wondrous features as multiple ways to encode form information, inline denormalized XML attachments inside a PDF-only datastream format, and embedded JavaScript.
To my knowledge (and I've been working with programmatically filling PDF forms this week), Adobe has the only complete implementation of XFA in existence, and I don't know of any open-source graphical client that handles it. (iText and PDFBox have partial support.)
It is important to understand that there is a difference between forms and adding text elements to an arbitrary PDF.
You can create PDF that are real "forms"; and those can be manipulated using evince, the default Ubuntu document viewer.
But when you want to open arbitrary PDFs to just put text somewhere; then you need the latest versions of the Adobe PDF reader - that comes for free; but only on Windows platforms.
So if that is what you need on Ubuntu, you could try to use the wine emulator and run that windows tool.