Or you can have both the Ceeb and SRC privatized. Imagine the CBC owned by Conrad Black.
Actually, the CBC also owns Radio-Canada (which has widespread support among Francophones
because it's a public broadcaster), so that's strike 1.
Strike 2: CBC/Radio-Canada is never going to be privatized - whoever does so would pretty much lose an election and not just from being accused of not supporting Canadian culture and the arts. To have that happen would only increase the concentration of media into a few hands, which to me is dangerously unhealthy.
Strike 3: CBC/Radio-Canada owned by Conrad Black would be horrible, especially since the man is in jail (where he rightfully belongs). That alone would be as bad as Silvio Berlusconi in Italy - only this time operated by an apologist for "Le Chef", which as a Franco-American makes me queasy.
Personally, I think a country is civilized if it has a public broadcaster - but then again that's probably because I'm a broadcast media enthusiast.
Now, Canada Post is a different story - whilst I do think that government should operate basic infrastructure as a public service, the Post Office I could actually see fulfilling your criteria. The problem - I don't know how.