batteries ... can't, by the inviolable laws of thermodynamics, be more efficient than the energy source that was used to produce them

The first time I read this I nodded in agreement, but on reflection I don't understand what you mean.

If by "produce" you mean manufacture, it is certainly possible to imagine arbitrarily inefficient ways to make batteries. You could mine asteroids for raw materials, for example.

I think you mean that it is always better to connect a load directly to an electricity generator rather than to use the generator to charge a battery and then use the battery to carry the load. The charge/discharge process will necessarily have costs, though one old analysis suggests that lithium-ion batteries have charge/discharge efficiency of 80-90%, and more recent sources say "close to unity."

But the whole point of batteries is to store energy for use when the generator is not available, so this seems like a minor criticism. An advantage of electricity is that you can produce it in the most efficient way available at any time and place and the end user won't notice. The first time I saw a diesel/LPG dual-fuel car I was impressed at the ingenuity, but it didn't seem like a win for efficiency.

The annoyingly smug Tesla vanity plates around here often have some variation of "N0 01L". WanderingEng tells me it's not really correct to say your electricity comes from any particular nearby power plant. If so, we are all around 63% fossil fuel, 20% nuclear, and 17.5% renewable.