Free trade of labor and free trade of products are not the same. The correct concept is free movement of labor, which you refer to later. Countries do not trade labor.

It is very difficult to get into Mexico and Canada to work. I know as I have done both. I am currently in a lengthy process to get a LMO to work for two days in Canada. Even if approved, I will need to purchase a work permit at $150C for the two day job. Twice in the last twelve months while trying to enter Canada on a NAFTA exemption that I have been using since the treaty was signed I was turned back at the border. A reinterpretation of the regulations led to my being returned to the USA and the need for an LMO that was not needed before.

For many, many classifications of workers there is no free movement of labor, unless one chooses to cross the border under false pretenses and take work without the knowledge of the other country. In that case, were I to do that, I would be a lawbreaker in either Canada or Mexico, subject to arrest, prosecution and imprisonment. That is the reason I work doubly hard to get the proper paperwork, cross at a port of entry, state my reason for entering the country and how long I will stay, and buy the proper permits. It is illegal to do otherwise.

It is also illegal here. But, a lot of folks do not seem to care or want to justify their actions with excuses or emotional reasoning.