What, exactly, do you think is a reusable rocket? You can't just land it, refuel, attach it to a second stage, and fire it up again. Everything has to be retested and tons of stuff replaced because the forces during launch, let alone reentry, are extreme. Until they have lots of data on failure modes in the reusable stage, they are probably ultraconservative with what parts they replace so I wouldn't be surprised if the cost of reuse is ~40-50% of the cost of a new one (on mobile so I'm too lazy to look up spaceX's official numbers).
SpaceX's stated goal is exactly that - turning spacecraft into something more like a commercial airliner. Quick inspection, refuel, send it up again within 24 hours.
The Shuttle threw away its fuel tank, dropped its SRBs into corrosive salt water, and needed all 35,000 tiles inspected every time. The SSMEs needed a full removal and rebuild.
SpaceX has deliberately gone with multiple, redundant, lower-performance engines that are easier to maintain and less sensitive to the forces of launch and re-entry. More like a Toyota Corolla versus the Space Shuttle's F1 racecar - and every generation of the Falcon (there've been five so far) incorporates lessons learned to make it more rapidly reusable.
(X) reusable vector
(_) non reusable vector
Technicalities of the hows doesn't change that reusing stuff was already done extensively