The conditions for equilibrium are one thing and the conditions for stability are a different thing. The cp is where we consider that Lift is acting. The moment about the cg created by Lift is determined from the cp. Unlike the ac, cp position varies with CL, being zero at zero lift and about 25% at maximun CL.
By the way, this whole subject has reminded me of an old confusion that I have regarding the aerodinamic moment.
I am not sure if it is the torque moment created by the wing along with lift and drag, or if it is a mere mathematical subproduct of considering lift as acting on the ac instead of on the cp.
If I may chip in ....
At zero lift a normally cambered airfoil will have a negative (nose down) pitching moment which is
a couple. This means that the cp at zero lift is out at infinity somewhere (not zero). As AoA is increased the additional lift can be taken to act at 25% chord. This is where it acts from theory and where it acts when measured in a wind tunnel. A symmetric airfoil will have its cp at 25% chord at all AoAs, even zero, because the pitching moment at zero lift is also zero. Cambered airfoils will have their cps varying with AoA but tending towards 25% chord at high CL as you say.
So the aerodynamic moment at any CL is created by the wing as a
combination of lift and zero lift pitching moment. For cambered airfoils the associated cp will be somewhere aft of 25% chord. The aerodynamic centre is defined as the point at which changes in lift (as a consequence of AoA changes) act. This, for low speed airfoils at least, is 25% chord.
As you say, the conditions for equilibrium and stability are different things. For equilibrium (trim) we need to consider the moment arm from the CG to the cp; for stability we need to consider
changes from the trimmed state so we are interested in the moment arm from CG to aerodynamic centre.
When AoA increases the incidence on both wing and stabiliser increases, but the wing generates an increased downwash on the tail so the tail AoA increases by less than the wing AoA - think in terms of 3 deg at the tail for 5 deg on the wing.
It should be clear from this that with the CG ahead of the cp, you will need downward lift on the tail to get equilibrium. Moving the CG aft will reduce the lift required until eventually, if you bring the CG aft of the cp, you can trim with upwards (positive) lift on the tail which then helps to offload the wing (for a given weight) and reduce drag.
BUT, moving the CG aft will also reduce the moment arm to the ac and thus reduce stability. Without going into theory, although the wing ac is at 25% chord, the aircraft (wing plus tail) ac is somewhere around 55% chord and this is what matters. So if the cp is at, say 30% chord you can fly with a CG at say 32%, get the trim drag benefits and still have a stable aircraft. You don't need FBW to get this, but it helps.