I've been reading about the early modern cotton trade and noticed that Indian merchants and bankers were making exorbitant amounts of money, and the states would get a large tax cut. Surely this wouldve made for healthily rich Indian states that could raise armies that wouldnt allow Europeans to strong arm them.
Yes, absolutely. The British system was in part so successful because Britain preferred not to take direct political control over India and leave colonial ventures to the British East India Company. The initial focus was on trade, with armed conflict to extend trade executed through British East India Company forces. This was, in effect, a semi-private army controlled by shareholders in London although HM Government obviously intervened to some degree given the vast capital flows returning to London. As time progressed, the British East India Company became a public-private hybrid (to use modern financial terminology) corporation with British Army regulars at the disposal of the Governor-General who managed the company's affairs. The Governor-General appointed Resident Agents, sometimes called Political Agents, who nominally functioned as envoys between Calcutta and the princely states but who, in reality, controlled the everyday affairs of the native court.
As the British East India Company continued to expand into the Indian subcontinent from their initial positions on the coast, several native rulers began to directly combat the British by sabotaging their affairs, leading to large pitched battles and, later, military campaigns as Calcutta sought to establish its supremacy. This did not go without controversy, even back in London. When Warren Hastings, the first Governor-General, executed a native-born tax collector he was impeached in front of the House of Commons for carrying out an extrajudicial killing -- that is, Hastings was tried by the Commons for murder as had no delegated authority from the Crown or from a native ruler to execute foreign citizens for crimes.
As time went on, the British East India Company only seized territory strategically and, later, as a warning to future Indian rulers. If a ruler accepted British sovereignty, he could continue to reign as a figurehead with an extremely comfortable life. If he fought the British, the Company would annex his land and hold it in trust.
This complex state of affairs continued until the Indian Rebellion of 1858, when the pretense of the British East India Company was done with and HM Government appointed officials to the Raj via direct rule through the Colonial Office.