You're confusing profit with needing to cover expenses. Those are different things. No one has ever expected Canada Post to be a net earner for the government, unlike other Crown corporations.
It’s similar to having a Military, but required it to pay for itself. It could also be applied to the Police, they don’t need to pay for themselves either. Making them need to break even, is stupidity of the highest order.
Sure, except we all get equal use of the military and (in theory anyway) the police. Making someone pay more for using more police resources would be an injustice, even if someone built an economic argument around it. I don't think you can make the same argument about the post office. Don't think about people sending postcards to grandma. Those are a rounding error in the mail volume. Most of the mail is: offical documents, bills from businesses and unaddressed ad mail (i.e. junk). What would happen if we didn't make them pay for using the service? Should the government subsidize corporate marketing?
Capitalism captured our Post office, and it shouldn’t have ever been in play in the first place.
No, scarcity of resources means we have to decide how much of a postal service we want. In Victorian days they had postal delivery multiple times a day because it was that active and important a service. Is it still that important today? Obviously not, because now we do once a day delivery, and often to community mailboxes. What is the right size for a modern postal service?