Synthetic methane requires hydrogen as an input, so all of the above applies to it, too. It also requires as source of carbon dioxide. Extracting carbon dioxide from the atmosphere is not viable, which leaves either scavenging CO2 byproducts from industrial processes and biofuels. Both of those are not in sufficient availability to produce synthetic methane at grid scale.
We already have excess renewable generation in several energy markets. And it's been the case for years, but the promised energy storage revolution has not come to pass.
We're also not going to run out of industrial processes that produce large amounts of carbon dioxide, at least as long as we still build things out of concrete, so if for some reason hydrogen is too hard to transport or store, we can pay the extra price of turning it into methane and use all the infrastructure that we already have for natural gas. We can even recapture most of the carbon when we burn the methane again.
Nuclear has got to have the worse scalability story of any hyped technology ever. Very monolithic system with tight integration between components. Hazardous materials. Complex science and engineering that needs lots of different highly trained people. Exotic materials. High temperatures. Enabling works with quantities in the millions of square metres. Processes that are difficult to model. Endless secrecy for national security. Very strong buildings. Harsh design margins. Sites in remote areas with absolutely no night life.
We should be optimistic about nuclear. But also apply optimism to other technologies and industries. If the petro-chemical industry want to make hydrogen work they will succeed. So will the battery industry and solar. If nuclear can scale than so can they.
Would this cost money? Yes. But it would likely cost less than a grid based on nuclear power plants. The key insight is that hydrogen can feed combined cycle power plants, which cost a factor of 10 less than a nuclear power plant of the same power output. So, one could (if necessary) back up the entire grid with CC plants at a fraction of the cost of powering the same grid with nukes. If desired, one could use simple cycle power plants, which (while less efficient) are even cheaper by another factor of about 2, or 20x cheaper than the nukes.
It's also worth noting that France is producing less than half the greenhouse gases of Germany, despite having significantly less renewables, because it has a serious nuclear infrastructure.
