There are a number of problems inherent to using cap and ball revolvers for hunting, especially mid or large game:
1. Most shooters prefer revolvers of authentic design. Consqeuently, this means authentic sights. Hunting requires very fine bullet placement, and these sights are not very conducive to such placement.
2. Chamber capacity is limited. Yes, the Walker and Dragoons have capacities of 50 grains of FFFG black powder, but their sights are atrocious. Also, bullet strike is above the target, because these revolvers were intended to augment the single-shot rifle out to 100 yards or so. This propensity to hit high above the target is aggravating in the game field, where one may forget to use "Kentucky Windage" and aim lower to put the projectile where it will bring a quick, humane kill.
3. Range is limited because of the shorter barrel lengths of revolvers. Few such revolvers will accommodate a heavy, conical bullet with enough powder to produce the necessary energy for a clean kill on large game. Some game departments ban the .44-40 with its 200 gr. bullet and 40 grs. of black powder, because of lack of bullet energy on large game. Most cap and ball revolvers would struggle to match that load, and definitely suffer from their shorter barrel producing a reduced sighting plain and lower velocity.
Interesting observation on Central Fire on old percussion tins. Odd that I never thought of that, as I've been shooting cap and ball revolvers for over 40 years.
I think it can be sucessfully argued they they are, indeed, center fire. Really, does ignition matter with traditional black powder guns, especially when you consider the use of flintlocks?
I can understand banning Sharps linen cartridge rifles from muzzleloading season, as they are really breech loaders. Would that they banned modern inlines, sabots, copper projectiles, smokeless powder muzzleloaders (a pox on Savage!) and other methods of cheating from muzzleloading season.
Perhaps a compromise may be reached for now, allowing cap and revolvers for hunting only small game. If this proves successful, perhaps it can be expanded to mid-sized game -- with certain caveats:
a. A minimum 40 gr. powder charge or equivalent.
b. A minimum of 900 fps muzzle velocity.
c. A projectile weighing at least 180 grs.
d. Sights adjustable for windage and elevation, so the bullet can be placed into a kill zone with greater assurance.
e. Lead bullets only. No sabots or jacketed bullets.
d. No laser or glass optic sights.
e. Black powder or Pyrodex P only. I fear that too many shooters would try to cram as much Hodgdon 777 into their revolver to meet the minimum, endangering themselves and others. Hodgdon does not recommend using its 777 in any brass-framed revolvers. Hodgdon 777 is intended to equal black powder pressures and velocities when used at a 15% reduction. Used volume-for-volume with black powder, it generates higher pressures than black powder and may strain the revolver, to the point of damage or danger.
Anyway, this is my take on using cap and ball revolvers for hunting. Your opinions may vary but these are the requirements I would recommend to the game department, if large game (deer, antelope) were to be hunted. I would not recommend such revolvers for hunting game larger than deer, such as elk, moose or bear. This would be foolhardy -- and the shooting sports have never lacked for fools, especially when it comes to loading your own gun.