Can a single private military company monopolize ALL war in a flint-lock fantasy?

What if every monarchy was stripped of all their militaries though years of depending on a single company? Said organization controls the research, manufacturing, and sale of firearms, cannons, and training.

Their infantry divisions are 'purchased' by local lords during conflicts and rebellions. This would mean that the mercenary outfits can/will fight one another if called upon.

My question is: How plausible is this scenario? What would compel the Kings to relinquish their standing armies in favor of this system? How would the Company maintain loyalty and power?

Bonus Question: What if the monarchies monopolized magic? What if their noble blood allows them to train spell casters in few numbers? Would this balance the power evenly?