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.