Why to use special purpose dsPIC?
Of course you can use any processor for whatever you want.  What Microchip is telling you with classifications like motor control, power supply, signal processing, etc, is what they aimed the peripheral set at.  For example, when controlling a motor a 4-way PWM module for driving each corner of the H bridge sepearately with dead time control, and maybe center-aligned options could be useful.  However, that's not going to help much in a audio graphic equalizer project.

Personally, I ignore all these classifications.  Instead, I use the interactive selector tool to find the most suitable PIC for a particular job.  That lets you enter your requirements, and it narrows down the list of PICs for you.  If you're doing a motor control project, you will probably end up with a "motor control" PIC, but not necessarily, especially if the project has other requirements.

Again, ignore the marketing babble and select a PIC based on what it can do for your project.