Parliamentary republics do tend to form less stable governments, but it's also true that you can really govern by compromising both with your party, allies, and opposition.
In over 50 years not a single parliamentary republic has turned authoritarian, in fact only Sri Lanka in the 70s has done so since world war 2.
Presidential and semi-presidential republics? They are all just waiting for the right person at the right time, from Turkey to Nicaragua to the Philippines to Russia, etc, etc.
I don't think any modern country should aim at anything less than boring, albeit unstable, parliamentary republics, with presidents that are not elected by popular vote (like in Germany or Italy) and have no executive power.
If your country is doing good, you likely want minor/middle steer adjustements, not radical changes at each new vote.