That's fair, batteries are somewhat useful for peaking even in a world powered 100% by fossil fuels so there's some infrastructure that can be shared. And even on a cloudy day solar output isn't 0%. But I'm skeptical the overlap here is significant enough to invalidate my basic point, though I admit it's a big simplification.

Reality is extremely complicated, so realistically the exact mix of solar + fossil fuels that makes sense is going to depend on a huge number of factors and vary from region to region depending on weather, fuel costs, construction costs, transmission costs, and probably a thousand other things I haven't thought of. The best thing to do is stay out of the way of both industries and let the market sort all of that complexity out.

I would speculate the result of that is going to be a lot more renewables than currently exist, mainly due to the drastic reduction in the cost of solar and batteries that has been occurring over the last few decades, but I don't think it'll be 100% or even 90% renewables either (expect perhaps in the extremely long term). Time will tell.

Yes, but if you need to have all that infrastructure anyway it no longer makes sense to compare the cost of solar+batteries with the cost of fossil fuels because you actually need to have both.

If you compare the total cost of solar with just the fuel cost of fossil fuels (ignoring its CapEx and non-fuel OpEx) that swings the equation a lot.

No, I'm saying infrastructure cost for 100% is the same as infrastructure cost for 100%. You can't build 10% as much fossil fuel infrastructure and expect it to carry 100% of the load when solar isn't working. And obviously I'm talking about generation here, not distribution.