I agree that you can't run on PV alone without storage, without a grid that circles the world. But that's not the situation we face. There are PV, wind, and hydro for generation, and a huge variety of storage options from pumped hydro and compressed air through thermal and batteries to electrolyzed hydrogen and derivatives.
Gas (methane) doesn't have to come from the ground. The price of electrolysed hydrogen is dropping. It's early days; there's a lot of learning curve ahead, so we can expect further falls in price. Once you have hydrogen you can use it as-is or combine it with air-captured carbon for synthetic methane and re-use existing infrastructure.
Electrolysis is quite complementary to solar. It uses DC voltage (direct from the panels); and PEM (polymer electrolyte membrane) electrolysers start in a second or so, so passing clouds and such are not a problem. Solid oxide and alkaline methods have slightly longer startup times so may require an hour or so of battery storage alongside the panels. Carbon capture is similar to these latter two as I understand it.