Why do tailplanes provide down force, if not for longitudinal static stability?
Because the safe situation is: a gravitational moment nose down, trimmed with an aerodynamic moment nose up. In all flight conditions. The critical situation is not cruise, but the conditions at low speed. 


At TO and landing the Angle of Attack is high: a nose up attitude, commanded by a downward tail force. Velocity is low, so the large force is achieved by a large upward deflection of the elevator and/or a negative stabiliser incidence. The AoA range is from around zero in cruise, to 15-20 deg nose up: the required elevator range is from zero deflection to large up deflection (plus superimposed manoeuvre requirements down &amp; up). The average required force is downwards.
You don't ever want the horizontal control surface to stall, but particularly not at low airspeeds = during take-off and landing, the most critical phases of the flight. Placing the tail at a lower average incidence angle than the main wing means that there is Angle of Attack margin: when the main wing approaches stall AoA, the tail surface has some AoA left before stalling. This implies that in cruise, if the wing has zero pitch angle, the horizontal tail has negative pitch angle. 





But despite the lower incidence, the horizontal tail could stall or partly stall, for instance in a sideslip where a large portion of the horizontal tail is in the wake of the aft fuselage. If it does, we want the aircraft to have a nose down moment, not a nose up moment. If the wing is not stalled yet, the lift force is now not in n.p.$_{fixed}$ anymore, but in a.c.$_W$ And that implies that in the above situation, the nose moves up and the main wing will stall as well. Only when the c.g. is in front of the a.c.$_W$ and the tail force is downwards, will there always be a nose down moment in a stalled tail situation.
And in line with 2. and 3.: it must be certain that there is a stabilising moment in all flight circumstances, at all airspeeds, all angles of attack, all angles of sideslip. That is hard to guarantee when the main wing is optimised for cleanest aerodynamic flow and the stabiliser is in the wake of the main wing: efficiency of the main wing will be higher in all circumstances. By choosing an equilibrium state where the horizontal tail produces a downforce, and therefore less lift with increasing AoA, this problem is solved and the guarantee can be issued, without any additional analysis required. Very good in the olden days of aviation, before CFD.


Note that all above considerations are not really a huge concern in cruise: can the horizontal tailplane ever encounter a vertical wind gust with a velocity that can stall it? The velocity triangle says no, this is not likely to occur in 10$^9$ flying hours. A large aircraft can apply Relaxed Static Stability in cruise: pump fuel to the tail tanks and reduce average down force plus associated trim drag to a minimum, because AoA at cruise is very low. Or trim such that the stabiliser has an upforce, like in the drawing where there is static stability. But at start and landing, the trim tanks must be empty!

The additional burden for certifying this situation is a more elaborate analysis considering gusts at cruise altitude and the influence on static stability: are there any vertical gusts at a higher frequency than 10$^{-9}$ flying hour that can destroy the static stability? Such an analysis was impossible in the starting days of aviation, it is possible now of course.