As users become more proficient, you want them to keep using your service, not start looking for something better and faster. Keyboard shortcuts allow frequent users to become more proficient in your application.
While the mouse is easy to use and a mouse base GUI is easy to learn to use, it is not perfect. One challenge of the mouse interface is that it requires accurate motor skills for placing the mouse of (usually) small targets. Because the mouse is free to move anywhere, these motor skills cannot be learned except for hitting targets in the four corners of the screen (they're of "infinite size" per Fitts law).
When the mouse was introduced, there were many opponents who felt that productivity would suffer. Productivity is of course also influenced by the amount of errors made by the user, and GUI's have proven to be successful in reducing errors. Still, power users can become incredibly efficient using only a keyboard.
A keyboard interface's main challenge is remembering the combinations. Since the keys are in fixed positions, one can learn to hit the right one without looking. An expert user, given time, will be able to remember the shortcuts. I.e. you can learn to be fast and efficient with the keyboard, but it's much more difficult to become better at using a mouse.
Expert users of your system will have their error rate reduced by experience and it's normal for them to want to become faster and more efficient at using your system. Especially when your application requires a lot text input, constant switching between mouse and keyboard seriously hinders your (sense of) efficiency. One reason for the design of the rubber mouse-"dot" in between the keys of a laptop keyboard (still commonly found in Thinkpads) was to reduce the time required for making this switch. Not having to switch "modes" at all would be even better.
See also http://www.ncbi.nlm.nih.gov/pmc/articles/PMC61470/. Google says they've found it useful and they have the data to prove it I'm sure. Taken from UX.SE: http://webaim.org/techniques/keyboard/accesskey and http://konigi.com/notebook/shneidermans-eight-golden-rules-interface-design/: "As the frequency of use increases, so do the user's desires to reduce the number of interactions and to increase the pace of interaction"
Personal anecdotal "evidence": my manual therapist absolutely flies through the administration GUI that they use. It's been the same for decades so he's had time to learn, and he doesn't even give the machine enough time to render each screen as he's hitting the commands on the keyboard.