Warning, somewhat off-topic.
Because I'm a bit geeky and noodle on the internet when having coffee, some examples of Just How Weird Canada Can Be:
1) In Ontario at least and I believe some other provinces, Reading of the Banns at church is not a substitute for a wedding solemnization, but can substitute for getting a marriage license prior to the solemnization:
https://www.ontario.ca/laws/statute/90m03
2) BC does have a system for First Nations Designate (as opposed to a Religious Representative) to solemnize and registermarriages. As far as I can tell, this is otherwise exactly the same as for religious representatives (and so my shorthand 'deputise' basically applies).
3) BC has some very specific language applying only to Doukhobors (a sect originally from Russia that refused to cooperate with government for some time). To summarize, it seems that the government recognized (registered) some Doukhobor marriages after the fact, and now has a system that they notify the government after the fact to get the marriages recognised - I suspect because Doukhobors either reject the idea of church hierarchy or nomination of representative with government, but don't know. This was clearly a compromise when the act was last modified, but you'd need someone with better history to get the full story.
https://www.bclaws.gov.bc.ca/civix/document/id/complete/statreg/00_96282_01#section12
Again as far as I'm aware, those are the only 'purely' religious marriages that would be recognised in Canada now, and even then, it's the civil registry that counts legally (i.e. it's no longer purely religious).
Sorry for this sidebar, just an interesting topic to me.