No, America (at least the ruling class) wants free trade because we can buy products from countries that pay their labor $3 a day vs. paying an American worker $10+ an hour to do the same job, making those products cheaper for us (i.e. the US consumer).
Also, reread your last sentence again....Trump does not have an obligation to make sure the Canadian steel or Taiwan chip industies are protected.
He has an obligation to the 77 Million+ US citizens (and by extension, the rest of the US pop. that simply doesn't realize any of this.) that voted for him.