Actually, it starts way before any of these - at the time of the initial system architecture and design. Using market analysis to define the overall functionality of the camera, you would start off with what you want it to actually be when completed.
The mirror and shutter assembly would only be the front end and mechanical assemblies, and yes there would be a physical limitation on how fast they can operate. But the real concerns are the sensor, sensor design, and the image processing pipeline software run in the processor. All of this is of course battery dependent, since you want to maintain the life of the battery charge over a reasonable number of images. So you start off with your battery budget and sensor size. Every component has a power budget that needs to be maintained. You also need to have a reasonable idea as to the amount of software processing that needs to be done (worst case, high resolution, high sharpening, high noise reduction, etc.) in order to correctly size your processor in terms of processor speed (the higher the speed, the more power it will consume per image) which maintains the image thruput processing. Also, you need to determine your buffer size in terms of buffering up a number of shots waiting to be written to the SD card (and this is SD card dependent), and also the amount of time required for either RAW, JPG or both.
Then in parallel with all of that, is the cost factors, along with parts availability. System architecture and design are refined and modeled, requirements written and refined, which flow into hardware and software being design and then developed and module tested on parallel tracks. Each of these activities are brought together in system integration and test, where the results are compared to the requirements/specification and the modeling results. There will be obvious problems - both functional and performance. These will be identified and reworked to varying extents in order to meet functional and performance requirements.
I tried to make it easy, but there are also custom FPGAs and or ASICs that are very custom parts that contain specialized hardware that is programmable is such a way as to speed the processing in ways that a general purpose processing chip could never compete with. This way you can speed up the processing and pull down the power requirements to a certain extent.
This is the general process for a reasonable new product development. To the extent existing designs are available and appropriate they are reused - which generally speeds the process along. Also, existing prototypes would also assist and accelerate the overall process too.
hope that helps...