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The hat's behavior isn't necessarily all that hard to explain, though. Momoka was mentally torn in half before her will was stuffed into those hats, after all, so they're both going to be a bit unstable. We don't get much personality from Mario's hat, but Himari's hat could easily be Momoka's id. All of her immediate impulses, with nothing throttling them back even if she regrets her words immediately after speaking them. It wasn't until both hat teams started wanting to help Kanba that whole-Momoka started to act coherently.
I'm still not sure what to make of the implication from episode 23 that the hats:Momoka::the rabbits:Sanetoshi. I mean, what did those two ever do except applaud Sanetoshi?
And I didn't catch the "worthless trash" thing, but maybe that's just because it doesn't stand out as much as, say, "will never amount to anything." I'm almost certain that the hat's sudden change at episode 23's end was linked to Himari returning her transplanted life force, though.
Well, what did Sanetoshi ever do that Momoka and the hats could not? Sanetoshi was able to keep Himari alive for a limited time, show a small number of people an illusion that didn't directly affect the real world, talk to people, and summon two rabbits that can carry things around. Similarly, the penguin-hat kept Himari alive for a limited time, showed up to two people an illusion that didn't directly affect the real world, talked to people, and summoned four penguins that could carry things around.
The rabbits might not have actually done much, but it isn't like Sanetoshi personally did much either. He spent most of his screen time egging on the normal humans into trying to sacrifice themselves for each other.
You seem to be matching up the bunnies with the penguin familiars, rather than the hats like I was. Though I guess some confusion is inevitable when one side has two tiers (Sanetoshi > Souya and Shirase) and the other has three (Momoka > the hats > Esmerelda and the HiFuMi).
You know, we never found out just how Momoka got her diary, either.