Expecting such an outcome is starkly irrational. Its exact opposite is far more likely, as evidenced by the fact that we're already well down exactly that road to exactly that destination.
Why on earth would it? The government is the engine of social cooperation. Losing faith in it puts you on the road away from civilization, not towards.
If I look at the groups in America who appear to have lost faith in their government, I see a lot of groups - Proud Boys, antivaxxers, antimaskers, anti-CDC people - who could not be remotely categorized as critical thinkers. Their behaviors have caused a longer loss in personal liberty because the pandemic continues. And, to look at the Capitol insurrectionists - there's not much accountability.
I just don't think there's much evidence that losing faith in government leads to any of those benefits. And my experience tells me that it does the opposite.
The public at large if it results in more critical thinking, greater liberty or accountability.