Usually the proposal is massive solar arrays, and maybe only producing during daylight hours to avoid battery costs, and spreading the upfront build cost over the solar array's lifespan. I think a lot of this falls down though when doing the finance, as people realize they can make more money selling the electricity to the grid rather than using it for their energy intensive project.

Above certain threshold of solar in the grid it’s not necessarily so. Also there are locations that are good for solar and available but have terrible grid connecting capabilities.

depends on where you are. California reduced the incentives for home solar to the point where it's more lucrative to mine Bitcoin with excess solar energy rather than sell it back to the grid.

A project like this is going to rely on using energy when it's so over-supplied to the grid that prices drop to near zero. Which does cause some financial challenges, as your expensive machinery isn't running all the time, but it's different to just the energy being worth something.

The physics are very possible. The challenges of scaling and making it economically viable, now thats another matter.

With the current trends in the economics of energy, the thermodynamics is not really a limit: the electricity you need is generally available cheaply (or even at negative prices) at certain times of day. The biggest issue is getting anywhere close to that thermodynamic limit, and the cost of building the equipment in the first place. Capturing CO2 from air takes a lot of surface area and a lot of energy before you even do the 'turn into methane' step, and because the energy is only available at certain times, you can't run your plant continuously so the initial costs amortise badly. Those are the areas that need solving to make this concept work.