The problem with fossil fuels is that they're incredibly energy dense. Gasoline has about 12000 Wh/kg of energy density compared to about 250 Wh/kg for lithium ion.
Space is hard, and the paradox of launching a rocket is that you need a lot of fuel to fuel an engine for long enough to escape the Earth's atmosphere and achieve orbit. All of that fuel adds weight so you need more fuel to compensate for more weight, which adds more weight meaning more fuel. Burnable fuels have the advantage of depleting as you burn it, so as you get higher your rocket gets lighter and therefore requires less fuel to pilot.
In case that's not enough challenge, in the vacuum of space there's no great way to propel a vehicle on electrical power alone. Wheels ain't gonna work and neither will propellers, and while solar sails appear to work, they offer such incredibly low specific impulse (thrust basically) that realistically no manned mission that isn't a generation ship can use solar sails
So in short, space is going to require fossil fuels for the foreseeable future. Hopefully we as a species can find the technology to make a fully reusable and renewable space program at some point, but until then we'll have to burn chemicals get vehicles off of this planet.
Additionally, right now, until another organization actually builds and launches reusable space vehicles (and can demonstrate the competence and safety record) SpaceX is the world leader in reusability. SpaceX is one of two members of the exclusive "has relaunched a space vehicle" club, shared only with NASA's space shuttle program which ended over a decade ago