Simply using public funds to employ a workforce rather than contract one would save the most money due to eliminating the need to house and feed shareholders and turn a profit, but voters seem to like the contractor profiteering model even if it eats the public purse.

NYC only has a big subway system because it gobbled up all the failing private railways over the years. LA used to have the largest rail transportation network in the world, it was private, and it too failed to turn a profit and failed. Transportation runs at a loss.