Canada Post doesn't really have any control over regulations of other postal administrations. If they know something is likely to be rejected by say the US Mail, I'd rather they tell me that up front and then make a decision.
What's maddening to me is the inconsistency sending within Canada. Go to the postal counter and you'll be told one thing. Prepare it yourself and just drop it into a mailbox differently than what told in person, and it goes through no issues.
I have to say, I've stopped using cardboard backing, and since then none have been rejected. Cards (usually 2 per to increase thickness) in a penny sleeve, then a 9 pocket page tightly taped. So far no issues either in delivery or damage.
But by far the biggest issue I have right now is the increase in theft, which is not just a postal issue sadly. Prior to recently, I can not remember anything ever being stolen in the mail. Since the fall, between TCDB and exchanges done outside this platform, I think I am at 13 or 14 envelopes which have been stolen. They're clearly not disappearing from the destination mailbox, as in each case I have mailed multiple envelopes on the same day and every one of them disappears. Somebody somewhere in the Canada Post logistics chain locally is clearly helping themselves to stuff they think may have value.