Vertical integration is one thing SpaceX does but its not unique and magical as many other space companies have tried the same without achieving results similar.
I will not attempt to break all the reasons for SpaceX success in this post, but its certainty more complex then just vertical integration. And vertical integration isn't absolute, in some cases they reversed their vertical integration again.
Team building by Musk, consistent having engineers work on hard project after hard project, willing to invest in a next generation even if the existing system works in the current market context (canalizing yourself), believing in increasing scale overtime (only when planning to build 100s of engine iteration makes sense) are just some of the relevant parts of SpaceX success as an organization.
People claiming Musk has nothing to with this or is just some irrelevant figurehead money guy are idiots. At the same time, the brilliance of the team he build ultimately is far more important then his own suggestion about ideas with engines.
In case of the engine its actually Tom Mueller who basically off hand suggested to him that to reach his goals, he would have to design something nobody had ever done on a large engine, and was only used for smaller engines (phase shut off). Musk jumped on that and imitatively said that this is what they should do. Mueller said he wasn't sure if it could be done, but since they knew of no other way to achieve the goals, the team went off and eventually achieved it.
Mueller himself said he thought going after this was a mistake and a less aggressive simplification should have been done, but said he proved himself wrong and it was a massively important innovation.
This shows some important aspects of Musk. Not that he is some genius that magically design an amazing engine. Rather that he listened to his engineers and gave them the finances and confidence that they could achieve outlandish targets, and continued to support them even if they couldn't hit the target instantly. We see this again with Raptor, they had a target in mind and followed every line of design to achieve something close to as good as a 2 fuel engine is going to get.
One can argue that this is just blind optimism and then throwing money at the engineers, and that is certainty partly a fair critic of this approach. It did not work with self driving in the same way at Tesla. But the difference is that with evolution of Merlin and Raptor he listen to engineers who proposed challenging ideas that were still iterative and he supported them.
I have followed Space for a long time. Musk isn't some magical unique genius, but he certainty isn't do nothing idiot some of his haters want us to believe.
SpaceX success deserve series study and SpaceX without Musk is basically really understandable as an institution.