I half agree with this. It is true for society as it is today.

But if there was no state, it would be in the rational self-interest of large conglomerates to use their monopolistic power and wealth to gain more power and wealth, not unlike a state, no?

This isn't an inherent problem with capitalism but rather with monopolies, however monopolies are bound to form in industries with high barriers to entry, and businesses in monopolistic positions have no incentive to compete for better products and lower prices.

What the best solution to this would be is certainly up for debate, but it can't be ignored as a legitimate concern.