Electrolysis can easily be done at scale. A couple of megawatts of electrolysis equipment is about the size of a shipping container. Many such systems are in operations right now and have been for a decade. The technology is fairly mature and reaches efficiencies of 70-80%. You also don't need salt caverns to store the hydrogen. You can store it underground without a salt cavern. Sure, there are losses, but they're not unmanageable.

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.