The problem with the system you're proposing is the assumption that everyone has infinite time, and probably also enough income to deal with the fact people are fundamentally selfish. The EU referendum is an excellent example of how people in the main do not do detail. Sure, partly this stems from a lack of civic education and arseholes like Boris Johnson systematically poisoning the well. But ultimately if you're asking people to decide on all law, how will you get consistency? Or should things be based on community? How large/small should said communities be? What happens when you cross a border? What happens if you just don't agree with what the local majority says? How do you deal with nationwide requirements for things like medical care, benefits/support for the less able, and even basic infrastructure?
I agree that the current system is a shitshow, but that's also in part because we have a very bad version of a variable system. A shift in voting system alone would be transformative.
One thing I will, say, though, is we have become a very apathetic country. I recall when I was at uni in the mid-1990s, a technician there said Thatcher basically ruined everything. The head campus was fucking us over, and no-one was doing everything. "Ten years ago, you lot would have barricaded yourselves in and negotiated something better." It rather feels like that with the manner in which people in this country are meekly surrendering their free movement rights, or allowing over three million EU citizens to be systematically shat on. (Most of my friends are sympathetic to these things, and voted remain. Almost none of them have even contacted their MPs, because they think it's just a waste of time. Not really. If an MP was swamped with communications, their own self interest at least would force change.)