The cavalry wanted the manual safety not only for holstering a pistol but to be used when a horse became unruly. The cavalryman could put the safety on so he wouldn't accidentally discharge a round while regaining control of the horse. It was not unknown for a trooper who failed to lower the hammer on his revolver to shoot his own horse, which tended to be both embarassing and possibly fatal to the rider when the horse fell and rolled on the trooper or thrashed around in pain.
JMB apparently thought that a half cock notch was an adequate safety, and he did not put manual safeties on his hammer guns. His shotguns and rifles, none of which had inertia firing pins, had only a half-cock for carrying safely. As noted, both the manual and grip safeties were put on at the insistence of the Army.
BTW, there is plenty of evidence that the lanyard loop on the pistol was used, not to prevent loss of the pistol by a cavalry trooper, but by military police to keep the pistol from being grabbed while trying to make an arrest. But I have never found any evidence that the lanyard loop on the magazine was used. If there was concern about losing the pistol during a cavalry charge, there should have been concern about losing the magazine, and I assume that was the reason for the loop. But when the subject came up on another site, I looked at dozens of pictures of troopers in training, at manuals, and at books on the cavalry. I could find no evidence that the magazine loops were ever used. I had seen references to lanyards with two or even three snaps, but no pictures, and experts in cavalry equipment had never seen any.
Another BTW, the cavalry didn't need to campaign for adoption of the New Service revolver; it was already the standard Army handgun, having been adopted as the Model 1909. The Army wanted a modern .45 caliber pistol and having no idea when (or if) an auto pistol would be adopted, the adopted the Model 1909 in that year. Colt chambered them for the .45 Colt, but the Army found the small rims jumped the extractor, so Frankford made the .45 cartridge, Model 1909, with a larger rim. (Those cartridges can be used in the Model 1873 only by loading every other chamber; that made no difference whatever to the Army, as the old single action was long obsolete.) Two Model 1909s were used as controls during the testing of the later auto pistols. In firing thousands of rounds right along with the pistols, the revolvers had two failures, both due to bad primers. There was no mechanical failure or breakage of the revolvers. The Army adopted the M1911 anyway.
Jim