I could be way off base here, but a couple of things occur to me. For one, I couldn't find anything but theoretical ideas about Falcon Heavy's or Starship's TLI payload capabilities. Elon doesn't seem to be focusing on getting to the moon, but rather Mars. The block 1B SLS is sporting a fairly robust 47T TIL payload. I suspect that, given their reported LEO capabilities that Starship would be comparable, but slightly less, if they were even trying such a thing.
Also, and here's where I may be way off, it looks to me like SpaceX is using a Earth Orbit Rendezvous approach. What I'm seeing involves multiple launches to refuel and resupply the rockets after launch. Project Artemis looks to be using the more familiar LOR approach, while also constructing a lunar gateway.
I'm not defending the stupidly expensive SLS system, or suggesting that we shouldn't be employing outside contractors for this. It just seems like Elon is doing something quite different from what NASA is doing.
Something else to consider. One thing we can be sure of is that people are going to die. Space exploration is risky business. While the underlying cause will almost certainly be the same, lax safety culture due to bureaucratic nonsense or corporate greed, one will likely be more palatable than the other. When NASA kills people we shake our heads and say "that was ridiculous. Don't do it again!" When SpaceX kills people, which I think is inevitable, I'm not sure how well they'll be able to weather the fallout.