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The state isn't irrelevant, but it's not the origin of everything. The market concentrates power on its own, and when that power is big enough, it captures the state to consolidate. Your own argument confirms it: if big corporations use thestate to grow bigger, it's because they were already big before they used it
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Also, regulatory capture and most barriers to entry are not market phenomena (at least not currently).
There are countervailing factors to scale, such that gains to increased scale are not always greater than the costs of increasing scale. Large corporations currently use the state to be larger than they otherwise could be.