But a prime minister is not remotely as powerful as a president. A prime minister has no independent power as he was not elected by the people but by the party

But a prime minister is not remotely as powerful as a president. A prime minister has no independent power as he was not elected by the people but by the party or coalition he/she leads. That party/coalition can in principle remove the prime minister any time they want. You cannot remove a president. Look at the attempts at removal of Trump. It requires an impeachment which proved near impossible. A vote of no-confidence is contrast is a very simple procedure.