I went through a couple of iterations of that post and hemmed and hawed about which way to go on the efficiency front, because there are pros and cons. As 0123456 points out, if you're trying to put things into orbit cheaply, a simpler and less efficient design can bring about big cost savings. On the other hand, as you point out, efficiency is really important if you want more delta-v to reach higher orbits.
Nasa was probably very focused on engine efficiency for two reasons 1) if you want to reach escape velocity for planetary missions, heck even geo-synch, then you need more efficient engines or more stages [with more chances one will fail] and 2) the US Armed Forces had a big hand in the design envelope of NASA launch equipment - most notably in the winged design of the shuttle to allow for high speed re-entry maneuvers - and the military wants efficiency because high delta-v is necessary to outrun/outfight hostiles.
Use of the shuttle for U.S. launches was mandated because the military wanted the private sector to help subsidize the super-expensive shuttle launch infrastructure. As competition from Ariane and Russia made that less viable to the point that the policy had to be abandoned, then US competition opened up for providing vehicles that better matched commercial needs, rather than military ones. It had nothing to do with public vs. private sector efficiency and everything to do with military requirements being imposed on all launches (including the majority of launches that had no need for those "requirements") and established players playing politics for legislative capture under the guise of national security.
Which is yet another reason why you should always be really suspicious whenever someone uses national security as rationale for black budgets and secrecy. It's really easy to abuse national security as a pretext for covering nefarious activities.