If the military were fair, then those who went to war would come from all races with a predominance of whites and of course all income levels and education levels. But of course without the draft, and even when there was a draft, that does not happen and it is not likely to as rich whites protect their interests and their kids.
No, recruiters should not attempt to make the demographics of the military mirror those of the country at large, because they should try to have the best army they can possibly have, regardless of demographics. The country is not going to be satisfied to lose a war because we had racial or gender quotas in the military. We also don't want to send old people or children to fight, just because there are old people and children in our country.
Joining the military should be an opportunity available to whoever chooses to take it. There should be no effort made to control the demographics for any reason. If a particular demographic group considers the military a path to follow in larger numbers than other groups they should be allowed to enlist in greater numbers.
The military can only do so much to attempt to get people to join up. It really would be wrong for them to have race and gender quotas of any sort, since this would potentially exclude people who want to join up, if they don't meet what's being sought. The military right now is voluntary and not based on a draft, so they basically have to take the people who voluntarily sign up.
Military service is a very large commitment that often takes service men and women away from their homes and families, sometimes for long periods of time. It should, therefore, be voluntary. Those interested in joining the military may or may not be an accurate reflection of the United States population at large, but no one should be turned away or accepted based on that fact.