No, they don't. As has been custom between the two countries for a very long time, the US $1 coin shares the same diameter, but different weight, as the Canadian Loonie.
The arguments against the Susan B. were well founded. The arguments against the Sac are just stubbornness to change (pun intended.)
We should have been out of the paper dollar printing business at least a decade ago.
Since when does the US do something because Canada does it that way?
Yikes!