Yes they do.
All I need is a valid US passport to visit Canada or Mexico at any time I want. I can apply for a job in either country and receive a work visa - and eventually a residency document - in either country. The employment part is more difficult in Mexico depending on what job you're trying to get, but if a professional firm in Mexico City wanted to interview me for a position, I could be in their offices tomorrow, no problem.
Border controls are for keeping out criminals, the insane, the communicably diseased and people whose presence alerts suspicion.
It isn't for keeping out normal people who want to visit or work.
Now this is simply drifting off into absolute absurdity, wideawake. Neither Mexico nor Canada (simply to take the two most obvious and geographically pertinent examples) allow U.S. citizens to enter said nations at will -- flagrantly flaunting their own legally established immigration procedures, mind -- and then to stay, indefinitely, in direct violation of their sovereign laws. Plainly, neither of these are [*kaff*kaff*] "police states"; neither then, demonstrably, is the U.S., in doing precisely the same.
ILLEGAL immigrants, on the other hand -- and directly contra to your own statement, above -- manifestly do NOT pass our borders with "valid passports"; do NOT lawfully "receive work visas"; and do NOT lawfully attain "residency documents." Nor, more to the point, would a U.S. citizen following precisely these procedures in Canada or Mexico be simply (as you so scissored my earlier, factual assertion) "entering said nations at will."
Good grief.
Let me guess. You are with the U.S. Chamber of Commerce which is America’s greatest advocate for open borders and modern day slavery?