That's not even the last step, really - it would prove that they could do it but that's it. What they really need to change the game is to get down full and rapid reusability. SpaceX estimates are that they could do launches at $7M if they could land a rocket, refuel it and launch it again. I'd say the "last step" is rapid, automatic and full rocket reuse, like an airplane. This is probably still 4-5 years away (at minimum) I'd guess.
I feel like that's a bit of an exaggeration. The cost savings isn't in Southwest-style 20 minute turn around. It's that you're not throwing a booster worth tens of millions of dollars away at each launch.
A rocket is not worth 10s of millions in raw materials, so it is the process of creating it that makes it worth tens of millions. So the 10s of millions of dollar question is: how much cheaper is the process of re-using a rocket vs the process of building a new one? It seems impossible to ever fully recoup the other 97.7%, but how much can they?
Well, it's both. If SpaceX wants the demand side of the market to expand sufficiently for its business model, it will have to launch that frequently. Also, the faster you can launch, the fewer rockets you have to build for your fleet.