I know some will criticize the Covenant as a far-right conservative throuwback; but if you read it, you'll see that it's nothing of the sort. While it might appear as a conservative step back to a bygone age, it was actually lauded by progressives in its time in the late 1960s. It's just that Canadians have since become so used to our far-left Canadian Charter of Rights and Freedoms that anything moderate now looks far right. Replacing the Charter by the Covenant would still guarantee Canadians' basic rights but without the far-left nonsense of the separate schools and excessive language rights, etc.
Also, even though the Covenant explicitly limits capital punishment to the most serious of crimes, still nothing would stop Parliament from maintaining legislation to prohibit it if that's what parliament wants.