SpaceX's greatest contribution has been to look at rocketry from the point of view of economics of running a rocket launching business as opposed to a "per launch cost plus" model realizing that fuel cost for launching a rocket is close to trivial compared to the facrication cost of making a rocket.
So their entire design philosophy is around reusability and reusability seems to push costs down low enough that you can get more payload up by simply doing more launches. While SpaceX is famous for not filing patents and instead protecting their IP using the trade secret approach and fabricating everything in-house, you can bet they'll be operating with more engineering headroom to get reliability and reusability.
Evidence for their bet having been right is the fact that they have grabbed virtually 100% of commercial and quasi-governmental launches and some part of US government launches. Other players in this space now almost entirely depend on defence contracts or national prestige contracts to survive.
Any rocket HAS to be very close to the limits of what materials used allow, and not the +50% margin of error you routinely seen in other fields. What you say about SpaceX is true, but only relative to the rocket industry as a whole. E.g. SpaceX uses cheap, available materials and simple designs over exotic composites and complex mechanisms. But they still operate close to the margins, as they have to in order to have any payload capacity at all. In fact, the move to steel probably reduced their mass margins even further.
EDIT: Actually maybe I shouldn't have used a car as an example: https://www.youtube.com/watch?v=pJdrlWR-yFM
"Have you got a spare billion dollars?"
"No. That's why we came to you."
_Lifting_ that fuel is NOT CHEAP. See also, the rocket equation.
But we're essentially arguing whether max payload per launch or payload efficiency to orbit is more important.
So yes, fuel is cheap.
With one and done you have a larger mass fraction to work with. Reusable spacecraft operate on much tighter constraints. Every single wasted pound in Space X’s design likely costs them 100’s of thousands of dollars in lost profit over time.
Reusable means cost savings, but it has a dramatic reduction in cargo capacity. This means more trips to get the same mass into orbit, which means mire fuel directly used and every extra lb in the design is then carried up multiple times while further requiring more trips.
Or, equivalently, in one trip with a bigger rocket you have left over from another launch, because you didn't ditch it.
Which again demonstrates reusability is really expensive, though clearly not always as expensive as a new rocket.
Remember while the first stage is significantly more valuable, it's not just a question of fuel the upper stage is destroyed with both approaches. So, combined with significantly lower payloads the cost per kg does not drop as much as you might think.
It doesn't make fuel cheap, let alone very cheap.
Actually another significant part of SpaceX business is modern engineering and modern mean of production. They used to launch without recoverability for some high orbit payloads and they were competitively priced for that too.