It's not only Office Open XML which uses zipped XML. Open Office's OpenDocument does the same behind the scenes.
There are a few advantages listed on the Wikipedia page on the Open Packaging Conventions:
Take the example of a catalog where a logo is repeated 1,000 times. Using an indirection mechanism, if we want to change the logo we only need to change one entry in one file, with no searching involved because we know where to look. This increases maintainability substantially. If you want to change the layout of, say, the ZIP directories where your files are stored, it becomes a trivial matter, because you don't need to know every element that can point to file, they are all in one spot.
It encourages documents to be split into small chunks. This is better for reducing the effect of file corruption. And better for data access: for example, all the style information in one XML part, each separate worksheet or table in their own different parts. This allows faster access and less object creation for clients, and makes it easier for multiple processes to be working on the same document.
Chunking also benefits programmers. Replacing one stylesheet with another becomes a ZIP file operation, not an XML operation. And it reduces the amount of things that a programmer needs to understand, because they can approach the chunks assuming that all the information on a topic is in that chunk: they are spared the mental toil of having to search through a big file with lots of extraneous elements.
In the Open Packaging Conventions each file that has reference has its own _rels file with the indirection lists. This makes it easier to cut and paste some information with all its associated resources in some cases, provides name scoping to remove the chance of name clashing between files, and so on.