Otherwise we're just rewarding companies (many of which are American) with access to our market without having to follow any of our laws.
What about the state of California putting tariffs in place on any company incorporated in state Delaware because Delaware corporate law doesn't have certain investor protections in place? I could list countless examples of US States that have less stringent regulations but still have free trade and open borders.
My point is that is impossible to harmonize all regulations and even if it was would have no clear universal benefits.
Have you ever wondered why all credit card statement comes from North Dakota? Or why companies are incorporated in Delaware? It's not because they have the strictest regulations. I don't hear Republicans demanding that we erect trade barriers between states to keep jobs where they started in the first place.
The truth is the Chinese population is willing to except regulations that allow awful environmental practices because the manufacturing that harms the environment is a significant opportunity to improve their standard of living. Let's not forget that only a few generations ago they were literally starving to death. https://en.m.wikipedia.org/wiki/Great_Chinese_Famine
Bringing the Chinese population into the global trading network resulted in one of the most drastic, beneficial, and impressive increases in standard of living ever. Better yet China is now moving to reduce the environmental impact by moving into higher skilled manufacturing.
If it doesn't bring manufacturing jobs back (which it won't) it will do nothing, but lower sales. the amount lowered depends on the size of the tariff, and how much that makes the products unaffordable to the locals.
So yes, in the end it does work out to be a penalty to the origin country.
The only local harm relates to marginal utility, but this is offset by the benefits of national security and improvements to the mix of different types of employment.
My opinion is that there should be tariffs to make up for the differences in laws anywhere without similar laws - if you want to pay workers pennies a day no problem, but you're going to pay the difference on the way in. China might let you destroy their local environment but you'll pay for the effects of your pollution on the way in.
Trade deals should come with negotiations that will help us with our global warming problem at the very least - if you want to have a trade deal you'll need to match or beat the regulations we follow or the tariff will reflect an approximation of the difference in cost.
I think that it is a bit problematic that the majority of those for free trade also want policies that discourage domestic manufacturing like an increase in minimum wage and increased environmental regulations.