I think the point is that your state permit for concealed carry is not valid on federal property. It is not just military installations. This is an area you do not want to misinterpret.
I work for the Army and I find the rules very confusing. All my weapons are registered on post and the acceptable transportation methods are not easy to understand when one just looks at the local regulations.
I keep it simple by not carrying or transporting firearms on post. When I travel, I will carry a concealed handgun, but if my destination includes a military installation, I leave the gun home.
Depending on the installation you visit, the response to discovering a weapon will vary a great deal. The response will even vary depending on the sensitivity of the facility you are near.
As to allowing soldiers to carry around post, it is a matter best left up to the commands. The soldiers are often young and wild. I would not want all the junior soldiers to be armed, but there may be a place for some. Again, the command will make the decision.