Really, there is nothing about a TN that prevents you from working in Canada, because you don't need any authorization for you to work in Canada (as a citizen).
But what you are suggesting sounds wrong. Do you plan on paying US taxes but not live there? Do you plan on not paying Canadian taxes?
If you are getting a TN to prevent your employer from having to follow appropriate processes for employing people in Canada it feels like you are putting yourself personally at risk for this employer.
Again, I am not an attorney, but you should probably talk to one about options here because something just _feels_ incorrect about this set up.
Edit: I accidently remoted a sentence:
There are many organizations (PEOs) that try to solve this problem, such as https://remote.com/