Good points Kieth, but M-95 Winchesters are a lot more expensive to build than a tubular-receivered boltgun, a major military logistical consideration, and they're already heavy. Beefing it up to make it more suitable for military purposes would have made it prohibitively heavy. M-95 muskets (The full-stocked military configuration.) are heavier than a Trapdoor Springfield. M-86's are also pretty massive actions, and the only other full-pressure action offered (Savages aside.) before the .308-capable modern-metallurgy-ed M-94 A.E. was the th M-71, a direct M-86 derivative.
They also have two-piece stocks, a notorious sticking point in early arms design-by-committee, the Lee-Enfield and Lebel rifles notwithstanding.
The K.I.S.S principle is an issue of primary importance. While the 1876 Winchester design, a HUGE, beefed up toggle-link action derived from the '73, is pretty simple, the '95 action, like the '94 and the '86, emphatically is not. Many people take leverguns to a gunsmith once a year for a detail-strip-and-clean because of their mechanical complexity. I've disassembled and re-built my '94, and can see why people would do this. The turnbolt is inherently simpler, with fewer parts.
The only levergun design that addresses the primary extraction issues is the Winchester Model 88, a lever-operated version of the M-100 autoloader. It's essentialy a lever-actuated turn-bolt design that is fully capable of withstanding whatever pressure ammo might be required, but it's a moot point, as the M-88 didn't arrive until well after the military advent of autoloaders. My '94 sometimes has sticky extraction with factory ammo, requiring thwacks on a springy lever. Palm-whacking a turnbolt handle applies worm-gear style force, a lot greater available mechanical advantage.
Straight-pulls like the Mannlicher M-95 use a helical camming motion to rotate their turning boltheads, but that's less direct, and not as powerful as yanking up the end of a boltknob. Most other straight-pull actions, the Lee and the Colt Lightning being excepted, use a similar set-up, and the Lee and the Lightning rely on pure muscle, a design issue that the large-frame (.45-70 class.) Lightnings never really overcame to the detriment of their sales. Modern straight-pull autos like the FAL and the Tokarev SVT-38/40 use enough brute force from their gas operation to pull through extraction grooves, making this a non-issue for autoloaders. However, if a case gets stuck on the way in because of deformity, like what happened to my Remington 7400 auto, you're out of luck. The Remington's a turning-head design, but had such a dinkum bolt handle that I had to pound the gunbutt on the bench to pull the jammed case out, as I couldn't get enough of a grip on the handle. Whacking my as-new rifle on the bench to free it made me wince, and doing that in a firefight is not an option, which is one of the reasons I really favor Garand/M-14 actions that have a turn-bolt style design.
Autoloaders with bottom-feed magazines pretty much put paid to the prone-use argument, making it time-contextual, although the Garand still allows such use, the only military auto that does. I'm not sure how relevant the argument is, but if I was a soldier, the ability to kiss dirt under fire while shooting back would be high on my list. Prone use of a levergun wouldn't be hard anyhow, merely requiring twisting the rifle, but a comittee might could object to the neccessity of un-shouldering a rifle to cyle it.
The inherent conservative-ness of military trials and procurement boards is a valid consideration. Mandating magazine cut-offs as an attempt to conserve ammo is a good example, and that grew out of an initial resistance to repeaters for the same reason. Committees are just that: committees. What they conclude doesn't neccessarily make sense outside of the committee. Arms committees notoriously have little contact or empathy with the common soldier despite the military origins of their members.
Just my rambling $.02. I'm all over the place, like usual.