Completely American myopic POV. Stable, healthy democracies that are unicameral parliamentary systems include Norway, New Zealand, Denmark, Estonia, Finland, Iceland, Lithuania, Portugal, and Sweden. (Most of those countries don't have strong judicial review either. Or federalism). That's without even getting into bicameral countries where the upper house is actually a lot weaker/just for show.
You don't have to separate the executive & the head of state, and you don't need to have checks & balances- that's propaganda for presidential systems. In fact I'd say the opposite is true- it's the countries with the checks & balances (by having a separately elected legislature and president) that are much more unstable and prone to autocracy. See Juan Linz on the Perils of Presidentialism