It was actually incredibly common for the English government (Great Britain didn't exist at the time of the formation of the great chartered companies) to authorize companies chartered with colonial enterprise to raise arms. This was because these companies operated in areas of the world where the English state did not enjoy a presence. They were carrying out colonial settlement in the Americas, trade in Africa and the East Indies (a catch all term for basically everything east of Africa). And to effectively do this they had to have the authority to raise and bear arms. They had to be able to defend their colonial possessions from attack by hostile native communities, from piracy on the seas, from regional powers who might have attacked them in their attempt to force themselves upon people who didn't want them and the useless crap they had to sell practice free and open trade with the world.

Over time these companies, particularly the East India Company, having armies also became a way for the British to fight proxy wars, notably with the French. The Companies were a force multiplier, with the state able to call on their navies and armies where necessary, pushing them into war as part of state action, but without the direct costs of having to maintain a standing army. That cost was on the company itself. This was particularly notable in the Seven Years War where the East India Company's armies had to fight proxy wars in India against French Interest. This war for instance is cited as one of the reasons why Clive pushed to conquer Bengal, out of a desire to prevent Siraj Ud Daulah from favoring the French. Later a similar issue prompted war between Mysore and Britain over concerns of Tipu's alliances with Napoleon/Revolutionary France.

Eventually the fact that the Company had armies, and more importantly, sovereignty over swathes of terrain greater than Britain itself came to Parliament's attention and caused discomfort. This led to an era of "scandal" over the unseemly wealth that Company officials could make known pejoratively as Nabobs. It was what had prompted the furious crusade of Burke against Warren Hastings, and eventually led to Parliament clamping down on the Company. Even so, the lure of Companies being able to act in British interests, but without placing obligations on the British state remained powerful. Its worth noting that in converting India to a Crown Colony, and promising them equal treatment as subjects of the Imperial Crown, Britain actually spurred the process which led to the eventual demise of Empire. Early nationalists in India cited Queen Victoria's proclamation in 1858 as the start of anticolonial rhetoric demanding equal treatment as British subjects.

tl;dr is that the British state got a lot out of having Private Armies who could be pressured to act to advance strategic interests where necessary, without having the obligations and costs of it on the Crown. It was not why Companies were authorized to raise armies, but it was why the practice continued for centuries after the fact.

Some sources on this.

The Sepoys and the Company by Seema Alavi

Naukar, Rajput, and Sepoy Dirk Kolff looks more specifically at the military market in South Asia. If you want to understand the context in which the Company's military system grew this is a good place to start.

The Colonial State: Theory and Practice by Sabyasachi Bhattacharya. More about the principles on which Company and Crown rule were based and the transitions from one to the other. Its not directly about the military, but the interplay of Parliamentary and Company politics comes from here. Its not really a military history, though it affected the military.