The problem is that there is no reason to be loyal to Heth, neither IC or OOC. OOC, the guy came out of nowhere, stomped on a bunch of canon upon which the Caldari RP community had built their roleplaying on for years, and generally contradicted everything we'd been told about the State since the game began, purely to start a war in a way that didn't make a whole hell of a lot of sense.
IC, Heth came to power in a way that did not seem to have any merit, and his entire regime seems to make him personally look weak; he's always been dependent on people like Oiritsuu or...the other guy that led the CPD and was assassinated I can't remember his name, and it's obvious he didn't get his position based on his own wealth, so that gives a reason for people to be suspicious of who is really behind his ascent. He risked the safety of the entire State for the sake of grabbing Caldari Prime, something that had been established as something only the most extreme Patriots even cared about anymore. He's stomped on the sovereign rights of the corporate powers.
I agree that it makes no sense that the CEOs supported him if they didn't want war, so they must have wanted the war...except that everything we were told until Heth took power is that none of them were interested in war, even the Patriots, and that's yet another reason them handing their power over to him is baffling. There is a reason why Svetlana has called them out for perpetuating this nonsense.
You also keep pushing this line that the Caldari seem to want to fight someone...this was not what the fiction pushed up until TEA; the Caldari were more afraid of being invaded by someone else than interested in starting wars; they skirmished among each other, but they had established institutions -- the CBT and CEP -- specifically to prevent the outbreak of an all-out corporate war. And war is an extremely expensive prospect when you have to pay for it, which the Caldari megacorporations would surely understand.