The Musk solution is limited to transport, where emissions can be reduced economically. Other emissions sources, such as steel production, will not be solved with the same mechanism, because no single company is going to suffer the competitive disadvantage of using clean tech.
Sucking carbon out of the atmosphere yourself will never be cheaper than letting other people do it, no matter what Elon's R&D departments do. We can't reach our climate coals without it.
If people are already buying something, like electricity or cars, then buying clean substitutes that are cheaper and better than older dirty products doesn't suffer from free rider effect.
Each person makes their own decision and gets more value with the clean option if it is better than the old product at what it does. The clean option takes over automatically thanks to individuals each looking out for themselves.
I used Musk's name as a short-hand for this approach targeting individual self interest because he has a very high profile in cleaner transport in the US. I did not mean to imply that Musk will somehow make CCS a desirable thing for individuals to buy. That's not possible.
Sucking carbon out of the atmosphere is not something that people get individual value from, or have been willing to pay for to date. So left to themselves, no-one would pay for it. That's why it needs co-ordinated action. Which we're not good at.
Yes, we can't reach climate goals without CCS. But it's going to be hard to scale up to approximately the same size as the global oil and gas industry.