A question I've always asked myself is how a corporation gets put on the Chief Executive Panel in the first place. To be more specific it has to do with Lai Dai and NOH since they were not part of the original six that took part in seceding from the Federation.
I've always answered that question with Lai Dai and NOH being part of the traditional power struggle between SuVee and KK and attempts to gain more control over the CEP and the State decision making process. Certainly it seems unsurprising either party thinking to themselves: "Hey, if we offload some of our subsidiaries into a new entity and then get them a seat on the CEP, more power to us." Only for the other side to react and do the same thing with the end result of having two extra Megas on the CEP but with the same balance of power.
I would say that speaks strongly for how power is distributed in the State. The Megacorporations are in most respects powers unto themselves and the Caldari State and its independent institutions exist solely for the benefit of their own interests. Even getting a seat on the CEP is dependent on the largesse of an existing Mega due to the amount of economic control they exert over the State. Hell, the Megas even back their own currencies in the State domestic market and probably conduct all sorts of manipulation on it to ensure that the wages they pay out get sunk back into products they make and sell.
Until Tibus Heth and the Provists there were almost no checks on the economic and political power of the Megacorporations in the Caldari State that were not self-imposed by themselves via the CEP. Because aside from banks like CFU (Which probably has restrictions itself on independent/private loans outside to the Megas) almost all capital in the State is centralized in the central bank/financial institution that is at the heart of each Mega. It's a deliberate system to ensure that power is retained by existing Megas and potential competition by rising corporations will eventually be bought out when they need to raise funds through an IPO in order to expand.
That is what I've always found interesting about the State. Externally, sure, the Megas are willing to show a united front to outsiders but internally I think the management and executives are focused on their own interests and shafting their rivals with backroom dealing, corporate knife-fighting and shady practices. In purely political terms, the Caldari State as it exists is just a very useful power structure for the Megacorporations to advance and protect their interests and what it promotes is a very driven, competitive and focused society for no other reason than that if people don't perform well and do their job then there isn't any safety net there to catch you and it's game over man, because you have no bill of rights and no courts of arbitration to appeal to.
That I think is why the Provists seem to have so much support in the State currently from the "common" worker because they were told if they worked hard, conformed and did their jobs as part of their corporation they would be rewarded. How the Megas distributed power in the State in their own interests and that of their shareholders made that promise increasingly more difficult to deliver upon until all that economic and social disparity just blew up in their faces.
My short, simple and incoherent view on things anyway. I just think it's a misconception to think that the Caldari State is a state in the traditional sense because it came into being solely due to the original six Megas during the Caldari secession and the only authority that has ever existed to check their power are the other Megas via the CEP. Or the attempts by the CPD, more recently. There is no independent "government" per se in the State because the Megas are able to govern their own affairs and that of their employees and jealously guard that independence individually whilst at the same time seeking to impose their own interests and views as well as increase their power over other Megas via the CEP. The political parallels of the State, I think, lie in feudalism or city-states with the Megacorporation being the modern incarnations of the Raata Empire's Clans/Houses/Families/Whatever they had for the Caldari.