I agree with what this portion of your post "
but wind and solar are also not finite " but I suspect that is the opposite of what you meant to imply in which case I disagree with your intent. If something is "Finite" it has distinct end to its availability or extent, The complete opposite of finite is "infinite" in which the is no restriction or end to the subjects extent. There is however n intermediate state where something may have of discernible or practical end, and or it might have some restrictions to its availability. Google suggests
- Indefinite: This is used when the limits of a situation are not clear or certain, even if they are known to exist. For example, the edge of a fog bank is indefinite because you can't see it, even though it is finite.
Both wind and solar power in terms of their practical availability fall into the
Indefinite categorisation.
No one should be under the illusion that both sources of generation can provide ALL the power we need 24/7 which is one reason we need diversity of generating capacities, and or storage.
Part of that diversity includes nuclear and fossil fuelled (coal gas, or even hydrogen) generating but one of the necessities of that is to ensure such alternative supplies are able to respond quickly enough to cover for periods when the other sources are unavailable. You cant have a piece of major equipment standing by indefinitely without incurring costs to maintain it and man it sufficiently to be able to have it rapidly deployed when necessary. These costs arise almost all the time, so when you see wind farms generating, we still have to pay to keep the gas generators at standby. so there isn't sudden massive increase in the stand down payments, they are in essence moved around to any other generators that are moved to standby.
There are reasons why some generating plant has to be turned off at times to ensure the safe and continued running of the countries whole electrical supply grid.
Small pilot plants are attempting to access "White" hydrogen, it is essentially accessed by fracking. Now there's another polluting process which has been shown to affect water supplies. Why do that when wind and sun can be used without producing any significant pollutions?