Seems like a big part of it is actually caring about cost - taking it into account during design, manufacturing, launch preparation, etc. Doesn't look like NASA did that until recent years, and even then only superficially.
SpaceX had their big contract with NASA structured as a fixed price contracts. Most other contracts are cost plus, where the contractor gets paid for their costs plus an additional percent for profit.
It shouldn't be surprising that traditional program costs have not come down, since the more you spend the more you make.