Regards a military take over from private agencies. It is not just by amassing weaponry, but by researching better weaponry. Once people might have thought a small bomb would not be a significant threat, but the development of nuclear tech, which could have remained secret, changed that. New types of weapons, even in small quantities could change things.
An example is automated self-modifying self-replicating weapons. Even rogue mirror-molecule unicellular life is feared could destroy the biosphere. An intelligent self-modifying self-replication weapon system could rapidly grow and outcompete basically anything out there, especially if no other similar system is brought online soon after. The benefits of overpowering all other social agents, is control of all the atoms and all the energy.
As for financing. The concentration of wealth from compound interest, barring inheritance tax, would eventually create quadrillionaires, who could use their personal wealth to finance arbitrary things.
Actually with adequate hardware, it is conceivable that private corporations, even under the current political systems, could overpower the nation states if they did develop such. Even the state itself, their black ops labs could go rogue if such weaponry was developed.
I expect the development of such final weapons, which can reshape the world at will, weapons of mass construction, or better said reconstruction, will be the final concentration of power, which will purify the world.