It's not "proven." At the 10,000-foot view, the magical market theory folks implemented their ideas about free trade since Reagan. And who is happy with the result? Tariffs were a core policy of the United States from Alexander Hamilton through Lincoln to the early 20th century and, empirically, they worked pretty well!

Tariffs are a tax that buys you (at least) three things, all of which are difficult to quantify, and usually overlooked by economists:

1. Security. You make your own bullets. You're able to make and maintain your own military hardware. When another country cuts supply lines in their own self interest, you have options to advocate for yours, either through trade, making it yourself, or, yes, even force.

2. Economic opportunity for your children and grandchildren. And no, not just "factory jobs" as is commonly sneered, but a community of experience and expertise. An engineer that gets to interact with the products they design in that kind of environment is a better engineer. A country that gets to see and interact with the products it makes has a sense of pride and better social cohesion.

3. Social buy-in and consequences for companies. A Chinese car manufacturer doesn't give a shit if cutting costs killed your grandfather. A local company has to, because the executives and workers are all members of the community. I was in Germany during dieselgate, and the sense of disgust at the company was obvious. They felt that.

These things are, imo, important to the health of any country, but they can only really be valued in retrospect. So yeah, tariffs are a tax, but some things are worth paying for even if what's being purchased isn't necessarily obvious or easy to quantify.

Tariffs are only regressive on the collection side. The redistribution side can be as progressive as you want, more than offsetting regressive collection if you wish.