First off, any military's support of a product has zero bearing on my selection of kit.
As to your notion that the CRF extractor causing case-to-chamber misalignment leading to reduced accuracy which is somehow tied to the military running push feeds only highlights a serious lack of understanding in basic physics and firearm design and operation. As others above have attested to, custom CRF actions can shot incredibly well! As to the mechanics of it all, a CRF extractor is passively resting around the case rim. The case will rest in the chamber as it is constrained by geometry and gravity. In the case of a push feed that utilizes an ejector plunger, the extractor is actively engaged with the case rim and is working in tandem with the ejector plunger to leverage the case within the chamber. The extractor and ejector system of a push feed is active and ever present. As stated before, some bench shooters and the like reduce the spring force or remove it entirely.
While I have heard arguments to the effect that plungers can impact accuracy, I have never seen them demonstrably rise to the point of overcoming the errors ( loss of precision) of all other factors (environment, ammo, shooter, build quality, etc.). Whatever minimal clearance that exists between the case and chamber (and this should be minimal with full length sizing and nearly zero with neck sizing) is forced into a 'misalignment' will be amplified by a push feed and minimized by any action not utilizing a ejector plunger.
My personal desire for the use of a CRF is because I reload and want to have my brass unscathed and in a nice neat pile. From my personal experience with a number of push feeds I own, they work wonderfully well when cycled at speed. But they throw the brass rather far and if cycled slowly can scratch and ding brass, though not always. Given that I my brass is upward of $4 a piece, I am happy to have them well taken care of so I can get the most bang for my buck.
As to the dings affecting reloading, I understand that cold working the brass during firing and maybe dents can eventually lead to cracks, pinholes and neck splits. Typically I have seen this more with repeated firings and not necessarily denting (though it is the exact same mechanism of work hardening), but that is just my personal experience. Even so, I do like to anneal the brass before running them through the FL sizing die to ensure longevity.