Am I being too obtuse by pointing out that a corporation, by definition, requires the legal framework of a nation to even exist? I'll point out again that these private forces need to have their training facilities somewhere, buy their weapons somewhere, etc.

Not obtuse, but I do think you are being naive.

We have private corporations today manufacturing our nuclear weapons and that has worked out fine without them "going rogue." Historically, private fighting forces are not unique or unusual in any way. So what exactly am I being naive about?