If it’s anything like the SLS it’ll cost 100 times as much and take 3 times longer than if was outsourced to the private sector.

Boeing was the prime contractor for the SLS core stage and upper stages, and Northrop Grumman builds the solid rocket boosters. The entire rocket was outsourced to private industry.

The military does not use or want the sls. They have been notable (and vocal) early users of commercial lift.

I can't find the source, but one reason why SpaceX can reduce costs more than NASA, is that SpaceX is allowed to fail. NASA has to underpromise and overdeliver on everything. Else it will result in budget cuts for not meeting targets or wasting money. Having such constraints, results in much higher costs. If NASA could "fail-fast" without fear of cuts, it would look very different.

Another point is that NASA also works as a job program for a lot of states.

Don't forget the cost of oversight either. Someone, somewhere, slacked off while on a government job, so now we need someone to watch everyone work, and we need someone to watch them watch them work, and then we need a council to decide on team 1 and team 2's efficacy in case they slacked off ever, and then we need a division to determine that the council is doing their job as well!

Commercial crew was a call for the private sector to fly astronauts to the ISS. 2 private companies were selected, one is flying currently, the other? Still trying to get there.

If this second provider was a NASA project everyone would be screaming how much of a waste it is. Conclusion? Space remains hard.

The private industry incentive must be in rubbish removed though rather than expensive, overuning and overbudget contracts for useless space providers like Northrop & Boeing (who are having the floor mopped with them by SpaceX).