Many folks are not that comfortable with the idea of working in or for the military. Yes, at some level we all support armies via paying taxes, selling them food, teaching their kids, etc., but the more direct their support the more uncomfortable many folks get. For example, actually stabbing enemy soldiers on the front line is more direct than most of us prefer. No doubt this discomfort at directness deprives armies of the support of many talented folks.
There are a host of reasons making an explicit distinction of this sort would be an awful idea.
First the very fact that you distinguished offensive and defensive military activity carries the strong implicature that you think it's important to draw such a distinction. The message this sends to everyone in the offensive part of the military is that what they are doing isn't honorable, moral and worthy of respect by society but something shameful that needs to be swept under the rug. Remember a huge part of the reason we (our other modern democratic state) can deploy the military as cheaply as it does is because of an implicit societal contract to reimburse soldiers with favorable social status/gratitude.
Also the last thing the military needs is these extra distinctions tripping it up while in the midst of a conflict. You don't want a contractor who is best able to serve a given need unable to do so because of this kind of lack of flexibility. Besides, even during a war of choice like the Iraq war if the public felt that soldiers were dying because some "defensive" employees were refusing to help on the offensive products the backlash would quickly erase the distinction.
Most importantly though because the distinction doesn't make sense. Hell, I don't think the distinction between civilian (whose economic output helps drive the war effort for a modern nation state) and a civilian who got drafted into the military is a sensible one to make much less this distinction.
"Obama increases Department of Offense Budget 30%"
At best you will just make them pay a bit more for the offence employees. Those who have some reservations about being involved in offence will have a price.
You cannot distinguish defense from offense, because the best defense is to make our enemies afraid.
I could derive a benefit by claiming to be more "offensive" or "defensive" with different groups? I can recognize a certain bragging right to claim some portion of service was "braver" than others (I usually talk up being around radiation, for example), but I've never seen an offensive/defensive split.
As far as the contractors are concerned, inasmuch as they're technical folk, some projects are sexier than others, but these already have signalling advantages with coworkers.
Up to a point, perhaps - but only up to a point: let's say that the military needs 50% offense and 50% defense. If fewer than 50% of the suppliers are opposed to working for the offense portion, then there's little point in making a fuss - as you point out, a little reshuffling and you're back where you started. But if more than 50% of the suppliers refuse to work for the offense portion, then no amount of reshuffling can resolve the imbalance.
Why don’t more parts of the military, and more military contractors, officially distinguish themselves as more emphasizing defense over offense?
The very fact that essentially all military contractors are called "Defense Contractors" (as opposed to "Offense Contractors" or "War Contractors") seems to imply that a lot of people do try to make that distinction. It makes them seem more essential, and less dangerous, to have around.
Now obviously a large fraction of "Defense Contractors" aren't really about defense at all, but that's another topic entirely.
I work for a defense contractor, and while I have a desire to be primarily on the defensive side of things, technology tends not to distinguish between defense and offense.
The problem you solve is fundamentally "see and shoot". If you are on defense, you see someone coming at you and shoot. If you are on offense, you see if you can find someone to shoot.
Anything you build to see can help you shoot, and anything you build to shoot needs to see. There's really no simple way to separate offense and defense for contractors..
The government doesn't want to admit that very little of the DoD's job is actually about "defense".
You seem to be trying to apply market principles to a military setting. I really don't think they are very applicable. The MOS with the highest IQ in the Army is the infantry, despite people's common perception. If you go into ROTC the most competitive MOS is infantry. That is where the accolades and the glory and the sense of duty are the strongest.
If you distinguished between defense and offense, the less talented would tend to converge on the defense. Talented people are usually winneres and, in the military, winners kill. It is the exact opposite in the real world so it's a lot better to signal yourself as a peacekeeper to civilians than as ruthless killer.
My own personal perspective - as a retired soldier - is that I'd be uncomfortable serving alongside somebody who had moral qualms about killing. Even Christians (turn-the-other-cheek) and vegetarians bothered me on a philosophical level; how can you pretend moral innocence while being employed as a killing machine? If someone doesn't want to take on that mantle, that's fine, but to take it on but not acknowledge it is hypocritical - it involves the sort of double think that the Geneva Convention's moral responsibility is supposed to avoid.
Heh, I wasn't the only one either. During my Basic, the day we got our lecture on who the Padre was, and his role, one of our instructors pulled the Platoon aside and informed us that - like it or not - being a soldier means you're a murderer.
As for the organization as a whole, historically it has been very difficult to train men to kill. There seems to be an innate aversion to killing within species, in the animal kingdom. Nowadays we use indoctrination and desensitization techniques such as blood thirsty chants, and human-shaped targets to overcome this natural aversion - the population which will now shoot-to-kill has gone up from ~50% in Napoleonic times to ~80% in modern times - and to be frank, I'm just as uncomfortable with this as most of you. I made a choice to overcome my natural inclinations (thought the indoctrination helped), because I enjoy violence; most of the kids that join up have some sort of nonsensical high-faultin motives in their head.
When it comes right down to it though, whether or not I'm in a defensive position, I wouldn't want to be surrounded by people who are afraid of blood on their hands. I need to trust even the mechanics need to help if the reds come over the wall.
If people were smarter, I'd say the reason would be that such a system would not much affect offensive abilities. Employees in the military, both offence and defence, are fungible. Each extra person who goes into 'defence only' would free up another person to move from defence to offence.
It's a framing issue. Deliberately neglecting to make this distinction makes it easier, at least rhetorically, to maintain the pretense that all military action is defensive.
Actually, this already happens. If you go look you'll find that military people explicitly make these distinctions, and have a fine grained heirarchy of offensive vs. defensive/support roles.
For example: regular Army, Marine Corps, Special Forces, Marine Recon, all of these have different reputations regarding the actual level of combat they might see.
When soldiers meet the first conversation most often entails exchange of highly technical data regard where each has served, what they have done, and with whom, partly as the usual human effort to link people into your social graph, but also to establish where they are on the spectrum of bad-assery.
Managing one's place in that spectrum is a big part of military life.
I think it would be possible to measure people's aversion to working for defense contractors by looking at the starting salary of engineers. In my estimation there is a 10-30% salary cut for electrical engineers not willing to work on DOD projects. I would be interested to see if that gap existed historically, and if it is similar across disciplines.
There is generally no such thing as "defensive side of war" when it comes to military resources such as people and weapons. Defense and offense are temporary tactical priorities, not innate qualities (with a few exceptions like foritifcations - but those are notoriously out of fashion).