Rocket fuel isn't gasoline, it's hydrazine. It's not pumped out of the ground, it's synthetic.
This is a good lesson for the carbon capture economics.
We know how to make synthetic fuels and biofuels. As a general rule, making them costs around the same as carbon capture. "Grow some plants or something" is actually one of the most efficient known methods of carbon capture.
Biofuels cost more than pumping crude out of the ground. They also cost more, in most cases, than electric cars. So if you don't care about CO2 then fossil fuels win over biofuels because they're cheaper and if you do care about CO2 then electric cars win over biofuels because they're cheaper. Basically nobody uses biofuels unless they're subsidized. But we know how to do it; we just also know of something better to use in 98% of cases.
Then you have the other 2% of cases. Like aircraft. Existing batteries are too heavy for aircraft and we don't know if or how long it'll be before we have sufficient ones. But we could use biofuels for that. Put a carbon tax on fossil fuels and that's what might happen, because for a plane that might be the most cost effective alternative.
So you say hey, maybe it'd be better to keep using fossil fuels in planes and then use carbon capture. If carbon capture has a cost similar to biofuels, that could be competitive. But it's not. Because biofuels produce fuel. With carbon capture you still have to pay to buy petroleum.
Hydrazine is not used very much as a rocket fuel. It's expensive, toxic, mutagenic, carcinogenic, flammable (not escaping that though), and explosive. It also has a freezing point too high to be used in space (MMH, monomethyl hydrazine, is used in spacecraft with NTO as the oxidizer.)
The best fuels for the first stage of launchers are hydrocarbons, due to their low cost and good density. And the first stage is where most of the propellant in a launcher is consumed. The cost of propellant becomes increasingly important as the cost of the launcher is reduced; for SpaceX it is very important. The use of cheap propellants also allows more testing of their engines.
Some launch systems fly on hypergols (hydrazine is one of them; it is not used in the West anymore as a main fuel, being too toxic), some burn hydrogen with oxygen, some burn kerosene (RP-1), a new system is coming online that actually uses methane (Starship).
And these were just the liquid propellants. There are also solid fuel rockets.
Hydrolox could certainly use all electric production but all of the others require hydrocarbons as their feedstock. Take hydrazine, it's synthesized by oxidizing ammonia and the main feedstock for ammonia production is natural gas and it's synthesis produces CO2 as a byproduct. So we're right back where we started. Why don't we just use hydrogen and oxygen? It's true that storage is a problem since hydrogen must be kept at cryogenic temperatures to remain liquid but a bigger problem is hydrogen's low density. Low density means more volume and that leads to inefficiencies in the size of the rocket. Methane is generally the better option and coincidentally could use captured CO2 as a feedstock.
This is a good lesson for the carbon capture economics.
We know how to make synthetic fuels and biofuels. As a general rule, making them costs around the same as carbon capture. "Grow some plants or something" is actually one of the most efficient known methods of carbon capture.
Biofuels cost more than pumping crude out of the ground. They also cost more, in most cases, than electric cars. So if you don't care about CO2 then fossil fuels win over biofuels because they're cheaper and if you do care about CO2 then electric cars win over biofuels because they're cheaper. Basically nobody uses biofuels unless they're subsidized. But we know how to do it; we just also know of something better to use in 98% of cases.
Then you have the other 2% of cases. Like aircraft. Existing batteries are too heavy for aircraft and we don't know if or how long it'll be before we have sufficient ones. But we could use biofuels for that. Put a carbon tax on fossil fuels and that's what might happen, because for a plane that might be the most cost effective alternative.
So you say hey, maybe it'd be better to keep using fossil fuels in planes and then use carbon capture. If carbon capture has a cost similar to biofuels, that could be competitive. But it's not. Because biofuels produce fuel. With carbon capture you still have to pay to buy petroleum.