Regarding flaws, the Brim Hats have so far been very underwhelming.
The author doesn't even vaguepost about them having coherent larger plans or schemes. They're basically impotent in most cases, or have no higher ambitions other than being sadists or cruel. They don't want magic to spread to the masses, so it isn't a question of isolationist "secrecy for the greater good" vs freedom for everyone, but just a conflict between people that want to be tyrants and basically everyone else.

The issues with the normal witch system being so flawed cause greater conflicts within the cast than any kind of philosophy from the Brim Hats themselves.
They are so far just thugs and psychos that the cast would coincidentally be grouped with if they ever fought against the system. There is no sense of them having a point, that they themselves aren't precipitating through violence and cruelty.
Their plans for Coco seem to go no further than, "if I break her friend's legs and throw him down a well, she'll have to break the rules to save him or something". And then Coco uses common sense and saves them in another obvious way.