I can’t see sponsoring rich companies as a politically popular item.

This is actually not enough for most industries. Building up a plant, knowledge and company takes several years. Without guarantees that the subsidies will be around that long it's very risky to start a new manufactory.

On top of that, production costs are much higher than the domestic (or international) markets will bear, and although access to capital is good meaning you could possibly automate away expensive labor, the cost prognosis of energy and materials is worse than many other places. Not to mention that subsidising a factory that doesn't provide employment or net tax revenue seems a dubious use of government funds.

That way only makes sense if you want to strategically establish an industry long term, to build up to unique capabilities. Such as the green energy deal which could have made the US both energy self sufficient and an international leader in the emerging renewable energy market, or Silicon Valley for the then emerging IT market.

Doing it for steel (a mature market) would almost certainly require regulatory pressures to guarantee demand, such as military contractors having to purchase domestic steel, while developing competitive capabilities (it's unlikely the US will be able to compete on cost of labor, materials or automation, so should leverage that low cost of capital on R&D)