Good idea but also a gross oversimplification.
You can't compare a parliamentary democracy with a presidential republic whatever the voting system. The president is an elected tyrant. It's a miracle one hasn't gone rogue previously.
A prime minister is a chairperson who only serves with the confidence of their party. In the UK and Australia PMs are routinely knifed by their own parties. Additionally the government needs to win confidence votes to govern.
Australia has a proportional upper house with some real teeth. They can bring a government down. But New Zealand has a unicameral proportional lower house. Optimised for different things. Many people say NZ is better but they haven't had a big constitutional crisis so who knows. NZ only gets labour or national governments despite proportional representation.