There's a pragmatic difference between recovering the booster over some period of time, vs literally parking the booster right where it took off & ready to re-launch within hours/minutes.
I can't see re-launching withing hours any time in the foreseeable future. Even once they're proven reusable each booster will need significant inspection and likely maintenance before being ready to re-launch.
> I can't see re-launching withing hours any time in the foreseeable future. Even once they're proven reusable each booster will need significant inspection and likely maintenance before being ready to re-launch.
Initially, yes of course. But if they manage to launch a stage 100 times and it always passes inspection and etc, etc etc it's not impossible that eventually you'll get to the point where you only inspect every 2 launches, every 3 launches, every 5 or 10 launches.
Once the ride to orbit costs: $100million/X + $Ymillion + $Zthousand
where X is the number of reuses
Y is the second stage cost
Z is the fuel, launch fees, refurb, etc
There's an experience curve (https://en.wikipedia.org/wiki/Experience_curve_effects) that shows you how much you'll save as you build more and more units and it's entirely possible that the (expendable) second stage could eventually get very cheap to the point where you don't want to spend $1 million (or whatever) going over the rocket for every launch.
If you're launching priceless (or very, very expensive) fancy space telescopes that cost tens of billions then the cost of a failed launch is very, very high. But if you're launching a bunch of food and you can lob another shot next week if it fails, and everything else is cheap enough, it might someday make sense.
Before you ask me if I'm crazy, please understand that airplanes do exactly this; you have to get your engines overhauled every few thousand hours and I'm sure there are inspections, but they don't tear the plane down and rebuild it after every flight. Once systems get reliable enough, that's a thing.
"Reusing the first stage three times halves the overall cost of launch. Reusing 9 times cuts the cost to 1/3. However, there is little benefit to first stage reuse beyond that… Reusing both stages just once halves the total cost of launch. In addition, reusing both stages four times reduces the cost to 1/4, and reusing eight times reduces to 1/8."
As you touched upon a lot of things in space are expensive because launch vehicles aren't reusable, once they are it makes sense to create cheaper and expandable payloads rather than multi-billion dollar payloads strapped to rockets that can't be allowed to fail.
The same stage probably won't be ready to relaunch but imagine an assembly line of reusable stages that land at the same facility where they take off and then head right into a service center. With enough stages in rotation you can have a near continuous stream of launches.