Turks famously used Henry Repeaters against the Russians at ranges under 150 yards, and single shot Peabody-Martinis beyond that with the Siege of Plevna
Yes but that was a highly unusual case of close quarter fortress defense. Infantry tactics of the late 19th century is quite different from what we are used to, one should not use modern criteria to evaluate their weapons selection choices.
I’ll point out two items. First, unlike modern infantry that has a great variety of support weapons to call upon and didn’t have to deal with targets beyond the range of their personal weapons, riflemen of that period usually only had their rifles to deal with all threats. They couldn’t fire on a distant enemy artillery piece with mortars, heavy machine guns, sniper rifles. Instead their officer would act like an artillery spotter and have the whole formation to fire in volley. Short ranged repeaters will not be able to do this.
Another problem was smoke from blackpowder obscuring the vision of your own men. Rapid fire would only generate an impenetrable smokescreen faster. This isn’t an issue for cavalry, but you’ll appreciate the infantry can only fire so many rounds before smoke degrades visibility and they’ll have to pause or reposition. Thus accurate long range fire gets you more bang for the buck.