Norms can be nice; a lot of people like it when they can depend on other folks to just behave the same way they would.
But they really don’t work in governments.
Firstly, of course, a government that runs on unwritten rules can never be fair. Sure, it’s great for the ruling class for whom those norms are in fact normal but it sucks for everyone else. Talk this way, dress this way, act this way and you’ll go far; be different and you’ll just be quietly shut out of the halls of power completely.
That really sucks.
A system depending on norms is also profoundly anti-democratic: who says what’s “normal”? The people currently (and previously) in power do, and there’s nothing anyone else can do about it.
And they’re weak; so, so weak.
Norms only work on people for whom they’re so ingrained that they’d never even think to do differently and on people who are concerned about the response they’d get when they break them. Nobody else particulary cares.
People who want the visible disaproval will break norms happily, of course (hello, modern Republican Party and Fox News! also hello, punks and juggalos!). Breaking the norms of some group can be a very effective way to gain status in a different group.
And so will sociopaths, members of other subcultures who don’t give a rat’s ass about your opinion and even mildly disaffected members of your own subculture. Norms really only work on engaged members of the same subculture that’s enforcing them.
And, man, are those thin on the ground outside the mainstream Democratic Party these days.
Laws; ya gotta have laws.
So, you can’t trust norms to keep your government under control or even functional; and you shouldn’t want to anyway. You have to actually have laws defining what people in government can and can’t be allowed to do.
And you have to actually enforce them.