Looking at the historical effectiveness of tariffs suggests they are not effective at solving this particular problem, although if you were proposing something different, such as a national sales tax which would be applied to different products based on their country of origin then I would agree that hasn't been explored. But more specifically, using the power of the state to impose taxes as a means of repricing the effectiveness of capital can only work when capital is itself priced on the same basis. Arbitrarily adjusting the exchange rage for Reminbi to account for price differentials can (and does) happen.
What is worse, applying the tax allows practices such as child labor to be "priced under the tax" which does nothing for the children at all. Effectively rethinking the system such that a good can be manufactured in the US or nearby at a cost that both allows the humans involved to have a living wage, and one which makes sweatshops impractical, solves both problems, both increasing the standard of living for workers here and removing the market forces that enslave children far away.
I recognize however the essential truth in your suggestion which is the limit on anyone's ability to make systemic changes in a market can only reach so far. Altering the economics through taxation or tariffs is achievable through fiat and one has to weigh that against the negative incentives it creates.
One of the things that "drove out" manufacturers in the Bay Area were a slew of environmental regulations which added cost to the process with no customer visible benefit. That pushed manufacturers to use the same process where they didn't have those costs. And surprisingly places that witnesses the environmental impact of these practices didn't preemptively implement those controls themselves. So we have identical environmental damage elsewhere which was regulated out in the US.
So a more interesting question for me is how do we rethink this stuff in a way that understands the external costs of the activity and works in a way that makes those costs containable?