This seems like a good way to find some initiatives through consensus. The main mechanism seems to be giving a "conversational veto" to everyone in the discussion. A "let's move on" button, basically.
I find that very interesting. It would certainly help with concerns that "my legislature does nothing". It might actually be an interesting mechanism for legislatures themselves to deploy internally to set agendas, though it would necessarily weaken the power of the factions that actually set legislative agendas (the majority party, the majority leader, etc.).
On the other hand, giving a strong and hidden minority veto also doesn't seem to help with the issues that actually divide citizens.
- Would not talking about Brexit anymore actually help the U.K.?
- Should the U.S. Congress not pass a budget anymore, to avoid balancing it?
- Maybe all legislatures agree to broadly humane treatment for refugees, but how would they agree on healthy levels and categories of immigration?
- The biggest divisive issue in the U.S might actually be abortion, which generally isn't debated so much as such. It's also clear that not addressing the issue isn't making the underlying problems go away.
- More broadly, would the U.S. have ever done anything significant about civil rights if consensus was required first?
EDIT: Maybe I'm a bit too pessimistic about civil rights... the constitutional amendment process does require two kinds of consensus for ratification. And many amendments did deal with civil rights.