It a pretty complex question.
The fact is that the Union *did* develop a mounted arm capable of mounting a shock charge against infantry. It was just in the process of developing. As an example, Minty's "saber brigade" in the Army of the Cumberland was perfectly capable of delivering such shock charges in 1863, but their situation was odd - he was a ex-British regular cavalry officer and knew it could be done and how to do it. By 1864 you see a much more powerful Union mounted arm develop as it matures beyond mere "mounted infantry" into decent cavalry.
Indeed, the inferiority of the Union cavalry in the East is largely attributable to the fact that the Confederates were true "mounted infantry" who discarded the sabre and carried infantry muskets. Equipped with Enfields they utterly dominated their Union counterparts with carbines (even if they were Sharps or Spencer armed). Mounted the Union sabres trumped the Confederate revolvers, especially in 1864-5.
Now, the Army of the Potomac's cavalry arm in mid-1863 may be capable of delivering a shock charge. Farnsworth's mess on South Cavalry Field at Gettysburg is for different reasons. He charged a skirmish line behind a stone wall that had been built up into a breastwork with fencing rails from elsewhere (broken down from the Emittsburg Road fences by the pioneers) that the horses could not cross, over broken ground unsuitable for cavalry. The one regiment that did break through fragmented and scattered and did not exploit the breakthrough. This is simply a failure of Kilpatrick who threw cavalry into an unwinnable fight.
Had Kilpatrick broken through and reorganised he had a chance to "bag" 10,000 prisoners. His cavalry was too green though.
As for the range issue - the problem is that whilst theoretically the rifle-musket had greater range in the hands of the untrained volunteers it was not used at much greater ranges. It is difficult to find any practical difference between the rifle and the smoothbore in the infantry firefight. In skirmishing, yes, but not in standup fights. Hence the debate over withdrawing rifles from the bulk of the Union armies and replacing them with smoothbores.