Because governments are responsible to their citizenry, the whole socialism part of national socialism you see; otherwise you're just being held at gunpoint. And true citizens soldiers? Are these professional or conscripts? Either way is irrelevant really, who to spend years training to be a scientist or a doctor when you go just join the army and be valued as a real person.
Yes, but citizenry is defined differently in every scenario. In ancient Athens a citizen was an Athenian, with both parents born in Athens, male, land owner, and military service was mandatory. Similar to the beginnings of America. Scientists and doctors would be government officials which would just be a division of the military, since it's a militaristic state. Obviously, veterans and soldiers would be held as heroes, so they would have more benefits. The socialism part only applies to the actual defined citizenry.
The society you just described needs a constant war going on to exist. And a government should harbor opponents because A. not everyone agrees with it (this is just not possible with any government) B. a strong opposition keeps it from doing stupid [censored] based on the mindset of "Oh nobody's gonna question this crap anyway and we DO have all this spare money and resources just LYING around. Heck let's grow a pair and build that giant gorilla statue made of solid gold!" (I'm not being literal here but you get the point) What you basically just described is a dictatorship. And don't think I'm the "The people can govern themselves perfectly well" type of guy (I'm a stout believer in constitutional monarchy), but this system is the basis of any Communist or Fascist dictatorship.
There have never been any shortage of wars. And yes, it can lead to a dictatorship, but Fascism is what they had in Italy.
Living in your ideal system sounds absolutely miserable. So tell us again why anyone but the already rich and powerful would want it?
I'm sorry. And because its good?