I have and use a flintlock extensively. The pans often have cast "wrinkles" in them. Kind of like a ^^^^^^^^^^^^^^^^ surface that is hardly visible or detectable on the surface. A few things happen. Micro-particles of unburned flash powder build up in the crevices. Moisture hides in these crevices. The "fire" upon ignition has to go through this little obstacle course to get into the flash hole. Having a mirror smooth pan makes it easier to wipe clean - removing both particles and moisture. It also lets the fire (and heat) travel smoother and faster across and throughout the pan, although this is mico-seconds that are hardly detectable.
I have smoothed the pan on my action with polishing compound and a pencil eraser, followed by a tight cotton stub on a Dremel at low speed. It made it shiny and easier to wipe clean. I can't tell any increase in ignition performance.
Some people swear this act is a total necessity. Others use the factory pan without issues for the life of the rifle. Nearly any time a lock gets "tuned" professionally a pan polishing is part of the procedure. If you can do it yourself inexpensively and easily it can't hurt anything. I am not sure I would pay for someone else to do this as a stand-alone task. Again, I personally did not see any "faster ignition" as you put it. There are other perks to a polished pan as stated but the speed of ignition is negligible if detectable at all IMO.
