Actually I find this page a bit unclear
https://travel.gc.ca/travelling/documents/dual-citizenship
Exception: If you are an American-Canadian dual citizen with a valid U.S. passport, you don’t need a Canadian passport to fly to Canada. However, you still need to
carry proper identification and meet the
basic requirements to enter Canada.
The link regarding "proper identification" is
https://www.cbsa-asfc.gc.ca/travel-voyage/td-dv-eng.html
and says If you do not have a passport, and are returning to Canada, the following documents can denote identity and citizenship:
Certificate of Canadian citizenship (issued from 1954 to present)
doesn't say that a copy of the certificate (rather than the original) is enough, so I was reading it as needing to carry the original certificate.
Look, it's pretty simple: the government REALLY doesn't want Canadians travelling without the "approved" Canadian citizen travel document, called a passport. So they're never going to say "hey just roll up to the border with what you got on you, we'll probably figure it out."
But that does not mean it won't happen that way.
As I said, the law is quite unambiguous: they SHALL admit Canadian citizens. If you can convince them you are, they'll admit you.
But as you mentioned, they do have databases at the border, and it seems they actually can pull up our information pretty quickly, so it does make sense that even a copy of the citizenship certificate should be fine. I actually had to travel back to the US by bus shortly after I landed as a PR and before receiving my PR card. When coming back to Canada, they already knew that I was a PR and said that they did not even need to see my COPR, even though normally they say that a PR returning to Canada at a land border without a PR card should show COPR.
And as I've been saying, in practice, they won't say in advance they will accept this, but if your docs are good, your case plausible, and they know you-are-you and can find you in the database, you will be admitted.
Also for US citizens they'd be let in anyway.
(Okay stuff happens it is possible something happens. But that's true with a passport as well).
Now note: I'd still STRONGLY recommend eveyrone travel with their Canadian passport. If you happen to arrive at a border when there's some terrorism scare or some other issue (computers down?), you might waste more time than you'd bargained for.
But those are long-tail possibilities, and if you can't travel with Cdn passport, well,s ee above, I've said my peace.