Well thought through and well written article and civil despite my disagreement with sections of it.
I fear you are in danger of feeling like you have demolished arguments in favour of the monarchy because you demolished Peterson. The monarchy is popular across mostly of the political spectrum in Britain and Peterson certainly is not.
I would make two remarks in response:
1. No analysis can be made of the monarchy without considering its replacement. A Republic could have a significant conservative or regressive effect on Britain’s politics and be more expensive. There are a lot of cons and failures in other countries to consider.
2. It’s possible to oppose the system (monarchy) but approve of an individual doing a good job within it (the queen), just like you can support democracy but hate the president/PM. I am surprised this isn’t really being done.