I loved this, especially because when I read comments that start with "It's math time", usually they go on to show how some "nice in theory" idea would never scale, but that's the complete opposite in this case!
Also, another thing that's good about these types of energy intensive industrial operations is they can essentially act as a sort of battery - it's a large load on the grid but (I'm guessing, someone correct me if I'm wrong) could potentially be more flexible with respect to time shifting: if it's a bright sunny day, crank up the furnaces to full speed, but if it's cloudy, back off. That helps make solar installations more economical if there is a good chance something will be there to take up extra power.
You're correct that the power required is quite big. It's actually one of the dead-spot in my comment. Supplying 135MWh for 37min is a lot. For example, the Jichuan Solar Park – China is "1,000MWh" and 90km^2 wide (I assume the number is the optimal output).
So, if we want to produce 1,888 millions tons of crude steel with solar panels, and assuming we can supply with Jichuan solar park 10 plants producing 300T of steel:
1,888/3 = 630 steel factory = 630 Jichuan Solar park = 56700km2. It's a bit larger than Croatia. For steel only. And it's assuming ideal production, only solar panel surface...So it could be Ireland actually.
As for the "nice in theory", my small demonstration is actually in this ball park, because the other dead-spot is that I account for electric production. It represent ~30PWh and worldwide consumption of energy is ~180 PWh (85% of those are from fossil).
So this 5% increase of renewable energy, of total electricity production, is actually swimming in those 15%.
There's another catch to your calculation: arc furnaces use scrap steel, which is only enough to supply 30% of the world's demand at this time. That's why 30% of steel is from electrical power. AFAIK most of the furnaces are already built in places with plentiful renewable power to take advantage of negative power prices. There are furnaces in Europe that operate only when the power is free.
Most of the world's steel is produced from ore, which not only requires three times the energy of recycling scrap but also vast quantities of carbon from fossil fuels to incorporate into the alloy. I believe there's a relatively new electrolytic process for the ore but at far smaller scale and it requires even more power.
Northern Africa has a lot of cheap land and a lot of sun. Wind, too. Steel can be then transported (it is already shipped across large distances). You would have to solve maintenance, but that should be doable.
The main obstacle for investment is political stability and alignment.
Also, another thing that's good about these types of energy intensive industrial operations is they can essentially act as a sort of battery - it's a large load on the grid but (I'm guessing, someone correct me if I'm wrong) could potentially be more flexible with respect to time shifting: if it's a bright sunny day, crank up the furnaces to full speed, but if it's cloudy, back off. That helps make solar installations more economical if there is a good chance something will be there to take up extra power.