I've got some Frankfort Arsenal .45 Colt cartridges marked F. A. 4-12. The rim style is more similar to modern factory .45 Colt cartridges than it is to the really old commercial stuff which has almost no rim. I can see how they wouldn't have been suitable for use in a revolver featuring simultaneous ejection. I have a Model 1909 and ought to try to dig out some old black powder .45 Colt cartridges with the small rims to see how they work with the extractor. Finding them would be a chore.

"So why didn't they buy revolvers in .45 1906 instead of modifying the .45 1873 for simultaneous extraction and smokeless powder?"

Perhaps it was easier to just buy "off the shelf." for a design that was apparently known to be an interim acquisition until the time the coming .45 automatic pistol was standardized. The Ordnance Dept. was still constrained to supply ammunition for the M1873 revolvers they had trotted out of mothballs in order to supply to units stationed in the Philippines. It was an easy matter to chamber the New Service design for the same cartridge as used in the rehab'ed "Artillery Models" then in use.