They need us more than we need them.
I think you hit the nail on the head. As a conservative, I understand the economic theory behind opposition to tariffs, presuming that the world actually acted as a free market. However, the reality is far from that ideal. The world market is not nearly as free and open as many presume. Various countries use all sorts of "protectionist" measures to manipulate their economic outcomes. Japan has done it for decades, and China certainly places strict restrictions and conditions upon any company that desires access to its 1.2 billion person market.
You correctly allude to the fact that the U.S. is the most coveted consumer market in the world, and that gives us leverage. No trade war would erupt, simply because anything that dampens the enthusiasm of the American public for consumption disproportionately harms the world economy.
The founding fathers not only favored tariffs, but intended for the federal government to be funded exclusively by them. We are a nation that possesses a wide variety of natural resources as well as the technology and knowledge to use them. There is no reason we should be as dependent as we are today upon trade with other countries. And we certainly shouldn't be permitting our manufacturing base to be siphoned off by the third world. Targeted tariffs, along with drastic reductions in corporate taxes and unnecessary regulations, would revitalize our economy. In the end, it's all about incentives. We need to create incentives for manufacturing in the U.S. and disincentives for moving manufacturing elsewhere and trying to sell back into the U.S. market. We also need to remove current financial disincentives that are preventing the repatriation of trillions in corporate capital. That is investment capital that could be invested in ventures within our country right now.