What an interesting question! No, I would be opposed to the idea. My first objection is that at present government (I'm not locating this response, it's in the abstract, geographically speaking) owns the military and can tell it what to do (please let's not get hung up about the nature of government). If it was a private corporation providing military services there is no way known that a contract can be written which covers every contingency. The corporation would find ways of wriggling out of its obligations for sure.

My other objection is that the corporation is driven by only one thing - the need to make profit. I would assume that the model being thought of is that government negotiates a fee for service after contract negotiations. The fee is received. How does the corporation make a profit like this? It makes sure that its costs are lower than the fee received, doesn't it? So it cuts its costs, guess what, first thing to go is maintenance. Let's keep those planes flying eh? We don't want them falling out of the sky on us.

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"There were no D-Day Heroes in 1973" - Cold Chisel Khe Sanh