Apolitical military in the mythical past: GEN winfield Scott, while on active duty, ran for POTUS as a Whig in 1852. MG George B. McClellan was actively opposing his commander-in-chief, A. Lincoln while in command of the Army of the Potomac and ran for Pres in 1864 (after he'd been fired).
Do we give up our rights as US citizens because we put on the uniform? some yes but mainly no. there is also a difference between the active and reserve components. Sen Lindsay Graham is a USAFR Colonel. there are still a few states that elect their Adjutant Generals and a significant number where the position is a purely political appointment. Note that a RC officer writing for publication does not have to get a security review of what he writes before it is published if he is (1) not on active duty and (2) not required to do so because of his civilian DOD (or OGA) job.
Strategy: I know one of the AWC faculty members quoted by Kohn here. But his complaint was based not on the issue of national strategy but rather on the strategies that officers produce by law and policy. Remember that the Goldwater-Nichols Act charged the CJCS to produce the National Military Strategy. Every unified command is required to produce its strategy by policy. Unless officers at the war colleges are required to learn to do strategy, how can they meet their legal obligations. (BTW I ran the SOUTHCOM Policy & Strategy shop in 1988 and 89 and was resposible for GEN Woerner's last strategy as well as GEN Thurman's.) In addition, the process of developing the National Security Strategy (NSS) - called for in the GNA - and the Defense Strategy (instituted by SECDEF Rumsfeld) requires military input.

Cheers

JohnT