The purpose of those structures is to prevent a razor thin majority from going off half cocked and doing something there isn't sufficient support for.
I think you need to take a look at federal controlled substances policy. Even with resounding majorities in favor of various degrees of changing things in a particular direction the small steps that everyone can agree on still don't get done. The incentive structure for implementing popular change is broken and the difference between 50.0001% and 60% doesn't change that.
I'm not at all arguing that those structures are delivering value in their present formulation, just that they are present, they are non-democratic, and that was intentional (so arguments predicated on raw democracy are either disingenuous or misguided).
I think I would argue that the simplest first cuts to untying the current knot are to rethink the whole "legal bribery of elected officials" thing and find a reasonable way to enable multiple parties so that coalitions can align along a more complex set of needs than two sets of (absolutist) wedge issues.
I think you need to take a look at federal controlled substances policy. Even with resounding majorities in favor of various degrees of changing things in a particular direction the small steps that everyone can agree on still don't get done. The incentive structure for implementing popular change is broken and the difference between 50.0001% and 60% doesn't change that.