So there's some mission overlap (on purpose) between the Navy's E-6, and the USAF E-4 and EC-135 suites. They go back and forth in terms of the Venn Diagram of capes, but they're by and large centered around support of the nuclear triad (not the 135s, the former two). It's not that the airplanes are kept secret on purpose, they're not a secret at all (the boxes and procedures are), it's that they're not popular with pilots.
Very much necessary mission(s), just oft-loathed by pilots because in the end, it's a mission of permanent posturing. Same parent reason we Bent Spear in '07 (and one of several reasons I didn't particularly care to remain in the platform). People get tired of the procedural practice bleeding absent the flying or ka-boom inducement. Somebody's gotta do it type of thing. Ditto for missileer morale. Plus it's run by the folks in the back, beyond the immediate "don't crash the bus before we send this beep and get that squeak" imperative lol.