The "EV company" he bought consisted of an office and a desk and a kit car. There was no design, not even a plan.
If it was so easy designing and launching rockets for 10% of the cost, why didn't anyone else do it? Why did nobody else make reusable rockets? Rockets that could land on the launch pad? The rapid turnaround and cadence of launches?
Musk did what NASA was unable to do.
BTW, the Saturn V rocket engines were scaled up V2 engines. The essential bits were from the V2 engine - cryo fuels, turbo pumps, nozzles cooled by the fuel, boundary layer cooling, baffles to make the engine stable.
The Saturn V engines were lovingly built by hand. Musk's engines are mass produced.
NASA is a government agency, the US government made SpaceX happen by pushing polices to privatize various aspects of the space agency. I'm not denying the Musk is a good business guy, but his imaginings have nothing to do with the actual work that happens at the companies that he owns. Mars is a neat sales pitch, but SpaceX makes money from mass producing NASA rockets and selling launch services to starlink (and the military version of starlink). The "vision" there is landing a juicy government contract and agreeing to mass produce a proven rocket design.