They do have a significant effect on accuracy, though, because you don't have an explosion going off in your face and there's less time required for the flash to pass through the touchhole. In the British trials of 1836, the converted flintlock recorded 1,280 hits and six misfires out of 1,520 rounds; the Brown Bess had 992 hits, 167 misfires and 45 cases of hanging fire.While percussion ignition would have made the weapon more reliable, and did make all black powder weapons more likely to go off when fired, they had no effect on rate of fire
You don't need to stand up to load a musket, though. The 1824 Field Exercise advised that "If in a very exposed situation, the soldier attempts to load lying, he will, after priming, roll over on his back, and placing the butt between his legs, the lock upwards, and the muzzle a little elevated, draw his ramrod, and go on with his loading without exposure, rolling over on his breast again when ready to fire".Ferguson's rifle had about double the rate of fire of a muzzle loaded rifle musket, without needing to leave a concealed prone position to do so.
Also, "rifle musket" is a term relating primarily to later guns that fire Minie balls. In this era, you have either a rifle or a smoothbore musket. The distinction is important when you come to rate of fire, because rifles required a tight fit between the projectile and the rifling of the barrel and, consequently, were slower to load than muskets.
I'm not an expert, but looking at schematics suggests that break action is less mechanically complex than either the bolt or block action. With fewer moving parts, you only have to worry about the gun latching closed and sealing firmly. That might be more achievable than the other, more elaborate designs with late-eighteenth century technology, while still providing a high rate of fire.how would a break action solve that problem?