We have indeed spoken before, and I did spend some time grasping the basics of your system. Not the finer details, as I am a Bear of Very Little Brain. But I do understand that your system is based on people putting in the work, demonstrating the capability and displaying the qualities necessary to advance.
In terms of its politicians, Canada seems unique, as it is in many other ways. Certainly here in the UK, once elected, politicians fight for their seats time and again. Some have spent their entire career on the back benches, while others become Secretaries and Ministers and eventually hope to acquire a peerage, allowing them to continue in the House of Lords.
I think the point I was trying to make, rather badly, is that the Prime Minister is first and foremost a Member of Parliament. Parliament draws its authority from the Crown and its mandate from the voters, and is the final authority. There is no person or institution in the UK that can overturn a decision made in a full Parliamentary vote, except for the courts, and even then, for an 'unlawful' or unfair law to be changed requires a vote in Parliament. Now the US President is not a member of Congress, and may claim -as Trump does- -to have their own mandate as being directly elected in their own right, which may or may not be at variance with the perceived mandate of Congress. I am given to understand that the President can veto legislation passed by Congress, but I am not sure how far this power extends. As regarding stalemates in a bicameral legislature, we resolved that by severely limiting the power of the Lords to delay or block Bills. Effectively, they can delay some Bills by up to a year, but other Bills can be presented for Royal Assent without even passing through the Lords.