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%.