Is the ARMY the only branch that as you get promoted,you are promoted out of your MOS (E-7-E-9)

No, in the Marine Corps, I have learned that there is a potential to be removed from your MOS once you make the leap from E7 to E8. For them, they can either track operations (stay within their MOS) as a MSG or they can track "command" (leave their MOS) as a 1SG. Once this promotion to 1SG is made, they will never go back to their MOS and will only be considered for SGM (our equivalent of CSM), whereas the MSG will only stay in their MOS and only be considered for MGySgt (our equivalent of SGM).

No. There are several career fields or career families in the other services which also coalesce or merge at the senior noncommissioned officer ranks. In some services, First Sergeant is an independent career field (e.g. USAF) not a duty designation, as is the E-9 (CSM) level.

USMC E8 (1stSgt) and E9 (SgtMaj) are INDEPENDENT Specialties not tied to feeder MOS's. They can come from ANY MOS. We don't transition "back & forth" to MSgt & MGySgt (Resp) like the Army does.

Additionally, several MOS have "feeder" MOS depending on the specialty fields, but it depends on what it is. 03xx (Infantry) feeds to 0369 at SNCO. 02xx (Intel) feeds to 0291 at MGySgt. There are lots of examples of this, because various MOS "chains" only exist at certain points (ranks/billets) and as you progress in rank you acquire the next MOS.