Oh, but they do. New Shepard uses liquid hydrogen, which is not a fossil fuel per se, but in practice hydrogen is currently made from fossil fuels. SpaceShipTwo uses HTPB which is a hydrocarbon oligomer, basically synthetic rubber, definitely a fossil fuel. Falcon 9 first stage engines use RP-1, a fancy type of jet fuel. The Starship first stage uses methane, a fossil fuel (although it could be made renewably as well). The Atlas V core stage uses RP-1 and the boosters HTPB. The Delta IV and Ariane 5 core stages use liquid hydrogen.

The energy in rocket fuel has to come from somewhere. If it doesn't come from renewables, it's probably from fossil.

For instance, most hydrogen production currently comes from heating up methane and steam for a CH4 + 2x H20 -> 4x H2 + CO2 reaction. So current hydrogen is just gas with extra steps.