There's no incentive to raise wages. At best it forces Americans to pay more for certain goods but the idea that that money goes to workers is indirect. These Chinese tariffs just increase the cost of Chinese goods so unless the US is second in cost, they cut into US profits but increase the profits of other global entities. In the case of steel, Russian imports are up.
It's not just John Q Public that sees increased prices either. Increasing steel costs hurt US manufacturing jobs that use steel. Because tariffs don't bring in any new money abroad, it's US companies that are footing the bill. The net gain to the US is zero or even less if there are less manufacturing jobs because of increased resource costs. Less manufacturing ripples back into less profit for steel.
Tariffs are important to keep certain industries alive locally.