There were at least three repeating rifle/carbines which could have made a huge difference, and did on at least one occasion -- the Battle of Franklin.
They were
Union cavalry often carried them, one reason they usually defeated Confederate cavalry.
But JEB Stuart was not killed at Yellow Tavern by a 5th Michigan Cavalry Spencer carbine, but rather by a 44 cal revolver.
Henry's were also used by some Confederate cavalry, in Texas & Louisiana, and also by personal bodyguards of Jefferson Davis.
So it strikes me as very, very odd that more leaders of the time never figured out that increased soldiers' fire-power could mean increased probabilities for victory.
Had the Union jumped on the Gatling gun as soon as it became available, the war might have been a lot shorter. Pickett’s Charge, for example, would not have come anywhere near success. With such weapons in Union hands, it would probably not have been launched.
The reluctance of officers to bring in new weapons is not at all difficult to understand. Such weapons were very often unreliable and all required massively greater supplies of ammo, which was a challenge.
Integrating new weapons systems into tactics was also challenging and many officers, not unreasonably, felt that the battlefield was no place for experimentation.
Union cavalry often defeated Confederates, towards the end of the war. The situation was quite the reverse in early years.