Rifle assault tactics stagnated in the years following the Civil War. In some ways they even retrogressed. Why this should have happened is unclear (though I hesitantly suggest a possible hypothesis in the final chapter below). Brilliant thinkers (Upton, Sherman, Sheridan, Wagner, Ardant du Picq) set their minds to the problem. Measured by tangible results, the efforts were barren and the 1898 Rough Riders who advanced in lines, shooting as they walked, would have disappointed Hazen's men or Wilder's.
Three late 19th century issues illustrate the intellectual sterility. The first depicts otherwise reasonable men twisting even the most clear-cut questions into weapons for a power struggle--in this case between militia and regulars. The second tells of theoreticians who found the correct solution but were unable to express it clearly enough for practitioners to understand. The third shows talents squandered on a bogus issue--an illusion projected by a bad paradigm.

Brig. Gen. George W. Wingate had imported English marksmanship manuals while a Civil War captain of volunteers. In 1871 he founded the National Rifle Association in association with William Conant Church of the Army and Navy Journal. Originally a vehicle to train New York National Guardsmen, the NRA promoted the sport and enthusiasm spread. Armed with editorials from the Journal and led by Brig. Gen. John C. Tidball (who believed Custer would have won had his men practiced marksmanship), enlisted men and officers of all grades pressured Chief of Ordnance Brig. Gen. Stephen Vincent Benet into releasing army ammunition for target practice.
Interest in marksmanship grew. The infantry manual provided marksman's buttons for the uniform collar. General Sheridan extended target ranges and increased skirmish drill. Upton's tactics were revised to add a section on target practice. Eventually "matches between posts afforded a welcome chance for travel. ... Officers shot on teams and usually had the top scores.families came along, so audiences watched any important match. Their wives regarded such contests as important social occasions.

Interest peaked around 1884 or so. Conservative officers had fought the idea of aimed fire for years and now gained strength. Some roots of the conflict were honorable, some less so. National Guardsman Wingate wrote a marksmanship manual. Regular Army Col. T.T.S. Laidley, Commander of Watertown Arsenal, plagiarized it. The Army adopted the Laidley manual; Wingate sued in civil court and won.
National Guardsmen consistently beat Regular Army units in competition and so some Army commanders forbade their men's participation. Wingate, in his manual, explained that regulars lost because they were not very smart. "Rifle practice is to a great extent a matter of judgment...and the more intelligent men are the better they will shoot. Thus both in England and Canada the volunteers have been found to shoot better than the regulars." Most regular officers would have agreed, but many felt that discipline and steadiness were the soldierly qualities. Intelligence or, worse, initiative were undesirable. Riflery, it seems, promoted individualism.
The idea appalled conservatives. They agreed [that marksmanship] magnified the soldier's self-
importance and prompt[ed] him to treat officers as equals. Discipline could only collapse. [They]
doubted that [marksmen] would go forward on their own and argued that any system that
surrendered control over enlisted men encouraged cowardice. ... And even if soldiers did prove
willing to advance, that could be a calamity. [In that case, they argued,] marksmen could not be
relied upon to halt when ordered.17

German doctrine of the time approved only volley fire. The more you aim the less you hit, they felt. Better to just tilt the rifle to the angle specified by the captain, and pull the trigger without looking along the barrel. A movement began in Germany to replace rifle sights with spirit levels, thus removing all temptation to aim.
By 1890, the U.S. aim-versus-volley argument had degenerated into a fight between the Guard and the Regulars and common sense itself withdrew from the affray. The Journal of the Military Service Institution of the United Statespublished a German paper "prescribing parade ground formations for the battlefield. Discipline and order were worth dying for, entirely apart from military objectives." Any victory won by individual initiative would be "meaningless, both personally and politically."A 1910 article in the Journal of the United States Infantry Associationdescribed the fictitious decimation of an American regiment whose colonel had tolerated "artificial rifle primadonnas" by a German unit volley firing by angle only. Americans thought too highly of technology to file off rifle sights and attach spirit levels, so instead the US Army studied mechanical devices by Capts. Frank D. Ely and William A. Phillips, which made inoperative any rifle in a company not held at the precise angle ordered by the commander. Scientific Americanpraised the gadget's advanced technology.
Marksmanship clubs closed. The Army discouraged the sport because even Secretary of War Newton D. Baker had been persuaded that it bred indiscipline and disrespect. By 1914, at Baker's orders, the NRA no longer received government ammunition.
One cablegram from the war in Europe reversed the trend. General Pershing watched as an American battalion attacked three practice trenches without firing a shot and fired off a scathing telegram to Baker. The chastened Baker told Woodrow Wilson:
[size=1]Dear Mr. President:
You will be interested to know that in a cablegram quite recently received from General Pershing
he tells us that careful study has caused him ... to take an entirely new view of the importance of
good rifle shooting.... [He] urges us to see that target practice is extensively used in our training.
This will confirm the opinion which [NRA president] Colonel [William] Libbey expressed to you
and, of course, completely upsets the view which I expressed to you.
Our arrangements are made to comply ... and in a very little while a large amount of practice
ammunition will be in the hands of the soldiers, and suitable ranges provided for extensive
practice.[/size=1]

Pershing celebrated war's end by inviting British, French and Belgians to Le Mans for the largest shooting match in history. The US Marines won.

The hypothesis is sobering, of course, because the scenario seems familiar.  In conclusion, I offer one last quote which I came across while researching this paper. Mercy stops me from naming its author, but it is from a Military Affairs article cited several times. The sentence reads:
[red]There is doubtless little of a practical nature to be learned in the thermonuclear missile age from the way men advanced against fire one hundred years ago.[/red]

An even later tactical manual, the 1917 Infantry Manual, repeated Hardee’s and Mahan’s maxims again about skirmishers use cover to an advantage rather than worry about perfect alignment.[58]  And the same instructions for sergeants to insure that the men remain calm and take careful aim without haste, and to ensure the men take advantage of cover.[59] Additionally, the 1917 Infantry Manual described how units moved by columns, but deployed into “line of skirmishers” for combat.[60]  The deployment method is very similar to Hardee. No use of the line of battle formation is retained in the manual except for ceremonies.[61]  The basic unit of men has been increased to eight in the squad, from four in Upton’s “unit,” but the principle is retained. The concepts thus survived even into the 20th century smokeless powder weapon era.