You're missing a giant factor here which is the possibility that the military might ally itself with an existing civilian faction in such a way that only half the country saw the coup as a power grab.

For example, let's say that the military made a deal with <insert the most extreme sub-faction of your least favorite party here>. Then they'd have people to install into the newly vacated positions of civilian economic administration, and in that, they'd have a way to motivate that faction to join them and support their legitimacy.