There's really no reason why we shouldn't have steel mills aside from that.
What's more likely, as I stated in another comment, is if you destroy their comparative advantage at a tariffed industry, the Chinese guy that had the steel mill as his best option now has to move to the next even shittier one. Tariffs are usually economically worse than zero-sum.
To answer the broader question, if you believe in markets at all, then demand creates supply, and supply for cheap (and therefore abused) labor is arguably at least in part responsible for economies like China being so shitty to your average worker. If all Western countries would e.g. slap tariffs on goods imported from places with poor labor rights, but they were specifically contingent on that (and not just a list of countries that our Great Leader has a problem with), that would put the pressure on the Chinese government to raise the standards to remain competitive. That would be the kind of tariff I would support, and I don't buy the argument that if we don't allow for such shitty jobs, the alternatives would be even worse - this is exactly the kind of attitude that creates a global race to the bottom that is the major driver for enshittification all around.
Closest I can think of is the Romans required a constant influx of cheap labour from outside their empire for their economy. When the flow stopped (diminished conquering meant diminished number of slaves coming in) that was a major factor in economic decline.
