I don't think that's true, at least it wasn't conceptually radical. People have noticed the cost of "throwing away" the lower stages for ages, and many approaches have been thought of how not to do that. Take the (partly) renewable SSRBs of the space shuttle program for example, which came down by parachute. Landing a rocket on its tail is also quite an old idea. NASA had several demonstrators demonstrating the concept in flight.

SpaceX took a lot of ideas which had been individually proven before, and then put in the work to perfect them and integrate them in a production ready spacecraft. That is important work and good engineering, but not radical. An aerospike had literally never been flown to orbit at that time (I think still not), so it would have been a way worse fit for the SpaceX method of developing the Falcon 9.

Radical in terms of economics, but also radical in its incrementalism.

Falcon 9 was a highly competitive rocket without reuse. If they didn't get reuse to work it would have been a successful project. Reuse of the first stage was a huge cost optimization that put it in a class by itself -- but they they did it radically reused risks.

Contrast that to the X-33 which would have required a large number of new technologies to all work to fly at all.

Fixed-cost pricing was also a radical innovation because it drove SpaceX to do everything it could to lower costs. It was known for a long time that reusing (only) the first stage was a good path to lower costs, the SpaceX business model rewarded them for doing it.

SpaceX is highly technically innovative but it's been so successful because technical innovation has been centered around cost reduction and practicality, not chasing high performance for the sake of high performance.

The SpaceX model might need change to get to Mars because of latency. You can launch a Starship to LEO, have it blow up, and launch another one in a few weeks. If a Starship fails to land on Mars, however, you have to wait another two and a half years to try again. Similarly, SpaceX runs everything by remote control from mission control which is great in LEO but to stick a landing on Mars you need something that flies autonomously.

As is landing rockets on the launch tower (or as SpaceX would say: catching them). And I might be wrong, but I believe they are the first to use a crane on the launch tower to stack the rocket. Usually you do that before you roll it out to the pad. They were also the first to fly a full-flow staged-combustion engine. Maybe that one was less radical because prototypes have been around for 60 years, but SpaceX were still the first to actually fly one