You missed a critical point that by increasing the charge rate of the battery you've also increased the load on the grid, exacerbating the original problem.
In Pakistan we have had daily blackouts for almost 15 years, though things were better in urban areas recently. Basically, everyone in the middle class has a UPS, with battery to power lights and fans for several hours. Except these are maybe 70-80% efficient. So, yes, the grid has had to deal with, in a very real way, with the increased power demand of millions of households.