I really don't think it's a leap at all. Electric cars are the future, there is ~zero doubt about that. Every single electric car needs to have a battery in it. Assume (extremely conservative) that every electric car would have a 20KWh battery and you've got yourself a free (as in: it would exist anyway) storage solution that dwarfs everything we currently have.
Easy example for Germany (where I have an idea about the rough numbers): 20 million electric cars (less than half of what is currently on German roads) multiplied by 20KWh gives a storage capacity of 400,000,000 KWh -> 400,000 MWh -> 400 GWh. Assume that you'd only want to use at 10% of its max. capacity at any given time, that's 40 GWh, i.e. more than half of the average energy need of all of Germany that could be provided for up to 10 hours.
Way more realistic numbers would probably be like 30 million cars, with each having a 60KWh battery, i.e. 1.8 TWh of capacity.
You surely will need to oversize. I don't know about a lot. As I said, bad conditions for wind and solar (and water and biomass etc.) can happen at a single place, but not so much over a large area. But either right now wind is already ~30-50% cheaper than nuclear, so I really don't see an issue in oversizing. I'm pretty sure we'll also see technologies like synthesized natural gas in the future - i.e. when there is too much renewable energy, a power plant synthesizes it into gas, when there isn't enough energy in the grid -> synthesized gas is used.
I'm sorry that I got your point wrong. Key for your actual point imo is again: right now. Battery costs are coming down big time. We are headed for an electric car future.
See my point about car batteries above.
This is a stupid scenario. No one argues that the world should be powered by just solar.
The idea of the car batteries has a few issues.
Car ownership can change wildly from city to city, let alone from country to country, China has by comparison to Germany barely any cars per citizen, same as with India.
People that have a car generally want to use it, and since you don't have 1 car per person, you have an issue.
Taking energy from a car and feeding it back to the grid in any way resembling efficient would be an issue to say the least, and if we assume we are talking about using it just in house, then what about industrial facilities, I have a 275kw generator, that powers something to close to 12 hours in some days, now I would only need 55 vehicles to power it for that time for a single day, assuming 60kw/h batteries, and honestly this is a really tiny facility.
With automation of driving I wouldn't be surprised if the amount of cars per people at least in more developed countries will diminish in the future.
Using electric cars as batteries isn't the most reliable plan in the world, and honestly would make electrical stability of a grid a complete nightmare to maintain even if it could be realistically implemented.
As for the point of using synthesized gas, as I said there are quite a few ways of storing energy besides batteries, even reusing old tunnels can work, but once again we come back to currently not really having a world wide solution for the issue, and if we go for renewable only, we really should.
When I gave that example I wasn't saying anyone is arguing solar only, but you can't exactly give an example that is easy with several types of renewable sources, first because with the exception of the sun, certain renewable sources might not even be available, secondly because how do you even calculate for that, which is ofc part of the issue, if you want a reliable grid, you need to have reliable energy sources, and renewable isn't reliable without some form of backup, hence energy storage, which once again isn't a problem now in the way we do things, because we have a non renewable energies as backup, and battery backup is just way way more expensive, we are roughly 400$ per kw/h in batteries, with the price predicted to half by 2030, that is still going to be really expensive.