While common sense seems to order your idea about privatizing the war there is a clear danger that is revealed in the following questions,

1."How would a corporation that provides security in wartime environments, in fact thrives in such environments, react to policies designed to normalize said environment"?

2. I would like to know what checks and balances you would introduce to ensure that the goal of any war that we Americans involve ourselves in, and use security corporations for, are being fought to create security in highly insecure fields and Peace in warlike ones?

3. What assurances do Americans have that corporations owned by Americans, built on the infrastructure provided by American tax money and nurtured by American business policies would fight only for American interests if they run counter the company’s bottom line interests?

I won't assume that you will infer from these questions all the dangers or all the solutions to problems your intriguing proposal implies. But please look into its deeper implications. It is my belief that we should fight any war against any organization that violently attacks primary American interests and our safety. But, it is dangerous to introduce into the American business environment corporations whose profits are enhanced by diminishing our safety and whose interest in a war is not on one side or the other winning but that there be no winning. There is no security company that wants you to feel safe. Their existence relies on continued hostilities.