I do believe that the Westminster system would be better if cabinet ministers did not have to be MPs. I don't know about how it works in Canada, but in some countries with the Westminster system, the number of cabinet positions is determined by the PM in which case the size of the cabinet does not have to be so unwieldy.
Probably most U.S. citizens don't know what the Westminster system it.
I think that you're forgetting that it's the civil service that runs things, whichever of those systems, & they're staffed with not only experts, but also have a long history in dealing with each & every organisation & nation. Policy is originated by party think tanks (containing experts drawn from both the public & private spheres), & mandated by the party Executive.
Ministers are literally administrators, sometimes enforcers, who are the public face of the department's policies. Unlike an appointee, which can happen in the second chamber, they have a democratic mandate, & poor decisions that they make can make them lose not only their ministry, but their seat.
I'd also note that at Westminster, the upper house is stuffed full of experts from every field.
It's not like experts ever agree though. How many Supreme Court rulings have been unanimous? Furthermore, aren't all democratic centres stuffed full of expert lobbyists?
I do see your point, but it's equally applicable to the private sector, where the chosen few are fast tracked to manage departments whose operations they no nothing about, & go on to lead companies where they haven't the first clue about their products or services from the grassroots up.
PS: for clarity, the mandatory healthcare insurance I'm talking of, is one where employees & employers both contribute a specific tax into a specific pot. Even the unemployed can do some voluntary community work that takes care of their contributions to the pot. A limitation on medical liability would ease costs.
I don't think it would provide better healthcare for those receivind it now, but it wouldn't be that far off, & is the decent thing to do.