I’ve seen flintlock pistols in action; more often than not, they misfire. If you do get a round off, you can’t reload the damned things, not on horseback in the middle of a battle. So you’re left with a fancy miniature club or a poor facscimile of a boomerang.
I’d hate to have my life depend on a weapon like this. The development of the revolver (and then the magazine-fed automatic) might have offered some advantage in really tight quarters (provided you had no more than six or seven assailants), but again, I’d prefer to avoid such situations.
But since you’re never getting engaged in melee during a caracole, it’s not a problem. Wheel away with the rest of your rank and clear the gun after you return to the end of the line.
The principle at the time was that cavalry wasn’t going to engage in close quarters. After caracole became impractical (because infantry musketry got more common and longer-ranged), cavalry resumed the classic tactic of charging to contact as fast as possible and attacking with either lances or sabres, after discharging firearms once to soften up their targets. Or else letting someone else distract the infantry (artillery, other infantry, etc.) and then striking a flank or rear.
The idea of the caracole was that you ride up to a group of infantry holding pikes, fire your pistols, and ride away (to reload). Ideally, you would be in no danger at all - if your pistols misfired, all it would mean would be that the volume of fire spat at the poor schlubs holding pikes would be fractionally less.
In any event, the type of pistol used for the caracole was not the flintlock, but the wheelock - less subject to misfire & more resistent to the weather. The reason they fell out of use was that they were infernally complex, and so very, very costly to make (and if something went wrong with them, you had to find an expert gunsmith to service them).
Besides, you can’t win a war by playing defense, which means at some point you have to go to the enemy and take his ground from him. That means getting close.