And it took something as modern and well trained and equipped as the Japanese Self Defence force to defeat the Arasaka para-military forces.
That's exactly my point.
A private/corporate "army" can certainly be a major player on the international scene. Why go to the trouble, expense, and vast amounts time (training, setting up command/logistic/communications.etc. systems) if you only need to "persuade" someone occasionally, hire mercenaries. But any major nation (Japan in your example) needs a standing army sufficient to protect itself and it's national interests. And a competent army ain't cheap and takes time.
Look at real world China, they REALLY want to be a major player on the high seas but it takes time and lots of money to build ships. And just having ships is fairly meaningless until you have trained crews to man them, it takes time and experience to generate a Chief Petty Officer or a competent Admiral. So you can maybe build a navy in 10-20 years, then it takes another 20 (minimum) to crew it with competent sailors.
No corp is going to invest that much for that long.