The prime minister in the UK is regularly kicked out by their party, and it's the same in most parliamentary systems. Liz Truss introduced ridiculous ideological economic policies that caused a bond market revolt. Her party kicked her out within the lifetime of a lettuce. This is only possible in a parliamentary system. Most of her recent predecessors were similarly if less rapidly removed. In the past 40 years, only three prime ministers lost their job at an election. Six were either forced out or resigned. Of those, arguably only Tony Blair left through choice.
The UK is not Canada though. You have the House of Lords, we have a Senate. We are a (con)federation, and that adds a whole new political overlay that the UK doesn’t have.
The executive power of our PM relative to the body politik is much higher. We don’t have a tradition of backbench rebellion, and the PMO often wields more power than the cabinet.
The point is that a parliamentary system doesn't need to mean an unchecked leader