Git is unnecessary here anyway.
Git is useful for collaboration of multiple people on the same project. Is law making a collaboration? Typically there is a single person which signs the bill into a law. But there is collaboration during work on the bill, though.
But I do not think that people who make laws want to write git commands in the console. They want the GUI (ideally integrated into Microsoft Word). And if we are making GUI why not drop git and use a traditional relational database for storing the data?
Git is useful for a single person, too.
You are right that the default UI of git is intimidating for normal people.
Saying 'relational database' says about as much about how you actually store the data as saying 'json' or 'xml'. Yes, you could use a variant of git that stores all its information in a relation database. (And in a saner parallel universe, git might have used something like sqlite internally, instead of hand-rolling its own formats from scratch.)
But the question of UI is pretty much independent from the question of how you want to store the data.