I think this kind of misses the point of the video, which was not about the technology of Apollo as much as it was the design principles that went into making the mission a success. Technology obviously is involved in that, but the argument for "do it like Apollo" is more a long form version of "keep it simple, stupid".
A good example of this is when Destin brought up the Apollo 1 capsule fire[1] which changed the speed and safety considerations at NASA. He cautions that now, before a catastrophic accident, is the time to make sure the best possible plan is being followed, simplify things that can be simplified, and get people to the moon and back safely. Something as simple as the choice to not use hypergolic fuels means there will need to be extra equipment to reignite the engines and redundant mechanisms for such a system.