re: Does throwing long loosen up things for the run even without a high completion %

No question. Good D/C's look for this on film, and if there is no threat to throw downfield, the SS and friends cheat towards the LOS for more run support.

When two teams are equal in talent, you have to find an edge. Sometimes the difference is having more hats at the point of attack. Alot of coaching is about getting your players aligned properly and putting them in a position to be successful. Coaches look for areas that they don't have to respect as much so that they can put more emphasis in others, so if you force them to defend every inch of turf then it makes it much more difficult to do.

Very similar to a hitter in baseball not having to worry about any breaking or off speed pitches, if he can sit on the fastball he will have more success.