We've already been there. The 18th and 19th centuries were largely like that. The great wars of colonial Europe were heavily financed by private money.

Corporations held the real power in the US from ~1870 - roughly the beginning of the industrial revolution - until the vast Federal expansion of power and taxation of the WW2 build-up and thereafter.

Rockefeller single handedly stabilized the finances of the US Government by pledging his wealth as a support prop to JP Morgan. That premise is laughable today. The Federal + State governments spend the equivalent of a Jeff Bezos fortune every week. Meanwhile the US military is radically larger and more powerful than it was a century ago, as are all the agencies of the State.

If you think corporations are powerful today, the reality is they're hilariously weak compared to what they were a century ago. Further, back then there were very few regulatory restraints on corporations, while the giants were simultaneously drastically larger in comparison to the Federal Government and as a share of GDP. Most of the state governments barely even existed financially.