Here are my two cents. In general, I think that these tariffs are a bad idea, but can be effective in making China behave better going forward with respect to trade in general.
As I understand it, China dumps steel and engages in unfair trade practices, in particular with respect to steel and aluminum (among other things). With respect to steel and aluminum imports, China is not the largest importer of such materials into the U.S. In fact, I believe we get more steel and aluminum from Mexico and Canada than we do from China. Right now the tariffs affect all steel and aluminum, and thus the lack of targeted tariffs doesn't seem to be appropriate.
Further, China doesn't pay for these tariffs. American consumers do. The price gets passed on down the line, and you and I end up paying more when we purchase in a finished product. How is that a punishment directed toward China ends up hitting MY pocketbook?
These tariffs hurt a lot of US manufacturers who have supply contracts with their large customers. For example, if someone makes steel blower wheels for draft inducers for furnaces, they likely have contracts to sell those wheels for XX cents per unit, based on a contracted yearly volume. Lets say $1.15 per unit for volumes of at least 2,000,000. They may have only a 10% margin on that product. Let's say you inked that deal on January 1, 2018, and steel cost you Y pennies per pound (however it's sold), and now my steel prices just increased by 15% (1.15Y pennies per pound). If you're running on small margins, you're pretty screwed.
Plus, if that blower wheel manufacturer has his primary competitor in Europe, that competitor is buying steel at a lower price, as it's not affected by the tariffs. If the tariffs don't affect finished goods, but instead only the raw materials for manufacture, the US manufacturer now has an economic incentive to move his production to Mexico, buy the cheaper steel there, manufacture the wheel, and import the finished product w/o the tariff and maintain his profit margin.
So this looks like a big transfer of money from consumers and other US manufacturers to the US steel industry. Doesn't seem like the right tool to address China's bad behavior.