I suppose, chuck it up as a difference of opinions. I don't have a problem with your statement in principle. It works in a hypothetical vacuum. I just have trouble imagining how a person with zero background in a subject matter can demonstrate mastery of a new-to-them portfolio. In order to make a good judgement based on the information provided by "others" (hopefully at least those "others" are subject matter experts in your hypothetical cabinet) a minister should at least be able to understand what is being presented to them. To me, that requires at least some level of technical understanding of the subject matter.
It would bother me in you hypothetical scenario, if your minister were presented with conflicting reports. On one hand, evidence presented by an expert. On the other hand - "alternative facts" presented by a political hack (Kellyanne Conway style). I would really hate it if that minister then, due to lack of knowledge in the subject matter, would judge those as equally valid sides of the argument. And then, making their decision through a 'political lens' enacted a policy based on the politically expedient "alternative facts".
Call me old-fashioned, but I like my ministries making evidence-based decisions. I like my doctors to have gone to a medical school. And just like during the Freedom Convoy days, I still don't think that a bunch of truckers should be dictating public healthcare policy.
I share your instinctual preference; but Ministers have rarely been experts in the field they regulate, that's the exception to the rule when it happens.
Lets look back at Ford's first cabinet. (note I could do this to any Liberal or NDP regime)
Minister of Health/Deputy Premier - Christine Elliot - BA. History, Lawyer. - specialty real estate law. (did have personal experience w/special needs children)
Minister of Finance - Vic Fideli - Founded an Advertising firm, later Mayor of North Bay (no degree listed in his bio, though he apparently 'studied' business at Nipissing)
Minister of Social Services - Lisa MacLeod - Degree Poly Sci, previous work experience, Pierre Polievres Riding Assistant.
Minister of Education - Lisa Thompson - Former General Manager of the Ontario Dairy Goat Cooperative.
Minister of Environment - Rod Phillips - MBA, worked at KPMG then as Mayor Lastman's Chief of Staff
Minister of Transporation - John Yakabuski - Former operator Yakabuski's Home Hardware in Barrie's Bay.
***
So, Health Minister was not a Doctor/Nurse/Healthcare Admin by education or training
Finance Minister was not a CPA, no Business/Econ. degree
Social Services Minister had no experience in the field nor on-point degree
Education Minister had no on point experience or degree
Environment Minister had no on point experience or degree
Transportation Minister 'ditto'.
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Not unique to the Ford government by any means.
As
@lenaitch noted, ideally, there are Assoc. Deputy Ministers and other senior civil servants in any given ministry with the relevant expertise to operate/administer/regulate same.
The Minister's job is more political 'The Art of the Possible'. Liase between the Premier/Cabinet/Treasury Board and your Ministry, generally as an advocate for the latter; but while communicating policy goals and expectations from the former.
As well as motivational, politicians aren't always, but should be charmers/good speakers who can inspire/motivate staff. They are the outward spokesperson of the Ministry to the public, and their office is backstop to which the public can appeal to rectify problems.
Its certainly helpful if a Minister has a background familiarity w/their file, but its not all that common.