Are any modern commercial airliners with fly-by-wire flight control systems designed with negative or near-neutral pitch stability so that they can take advantage of the capability of such systems to reduce trim drag and increase fuel efficiency?
If so, which aircraft are so designed?
And if not, why not?
In the images, the aircraft with positive static stability must produce sufficient wing Lift (the green arrow), not only to hold the aircraft up, but an additional amount to compensate for the lift from the tail surface, which is pulling the aircraft towards the dirt. The total aerodynamic force is the sum of the Wing Lift plus the tail plane lift, which must equal the weight of the aircraft plus twice the lift produced by the tail. THIS MEANS THAT IN AN AIRCRAFT WITH POSITIVE STATIC STABILITY, THERE IS SIGNIFICANTLY MORE TRIM DRAG AND THRUST REQUIRED.
In an aircraft designed with negative static stability, (bottom image) The wings, (Green arrow) plus the tail plane, (blue) both contribute to positive (upwards) lift, and so the total aerodynamic force is less, therefore the induced drag is less, and the thrust required (and fuel flow to generate that thrust) is reduced in comparison to an aircraft with positive static stability..
if you would like more details, review this video, from which I quote (at about the 1:00 minute mark), speaking about general aviation aircraft with positive static stability, "... Something not very pretty about this situation, [positive static stability], is that we have this downwards acting lift force[ at the tail], which we call Trim Drag, which essentially, in a negative way, impacts our range and endurance, and which we'd like to avoid...", and then later, talking about the negatively stable F-16, at 1:50 minute mark, "In this situation we have, [at the tail], an upwards facing Lift force. This means ... we have, as it should be, all the lift facing UP. This means [my italics], we have an increase in our range and endurance performance.."
And, in addition, from this link, I quote "unstable designs get a slight reduction in drag and a slight increase in lift". The rest of this article is also very informative.
To further illustrate the difference, below are two photos, of aircraft on final approach to land, where the flight path is stable and descending.
1. An F-4, with positive static stability, and 2. an F-16, which has negative static stability. Note the relative positions of the stabilators on the two aircraft, and especially, the relative angle of attack of the stabilators as compared with the AOA of the wings. In both of these pictures the aircraft is descending to land, so the relative wind is from the left, and below.