The idea behind QuickPress was a fast posting option that did not carry the full functionality of the Write screen. The original intention was for the module to be configurable, so given the ability to put x number of fields in the module, the user could choose which ones, but that it would be limited in number so it wouldn't just be a duplication of the Write screen in a too-small space. We started out with tags instead of categories because with the use case we saw more people using tags than categories. Again, the intention was that it would be limited but configurable.
In mid-October we tried to add categories, but the interface for selecting categories is different (currently) than for adding tags, and we realized that we didn't have time to add categories to QuickPress and make it work right, so for 2.7 QuickPress is limited to tags. If that makes QuickPress useless for anyone, well...
1) You can hide the module until 2.8 and pretend it doesn't exist yet;
2) Maybe someone will write a plugin to add categories; or
3) Use the traditional new post screen, which has all the features including categories. It's one click from the Dashboard, and it's easy to bookmark in your browser so you can go right there without even stopping at the Dashboard.
And in 2.8 (February), you'll be able to add categories using the new QuickPress module.