I fail to see how the latest criteria ... relates to that (there's nothing there about tail or wing setting angles, just (indirectly)angles of attack, which aren't the same thing)
MFS
It is undoubtedly true to suggest that one could achieve the same tail lift coefficient with different tail setting angles for fixed horizontal tail surfaces, simply by requiring the use of elevator deflection. One could, in principle, select an angle for the tail with negative longitudinal dihedral as measured by that incidence, where the lift coefficient criterion is satisfied by having the elevator sticking up like an air brake.
But in selecting a tail setting angle, a design that requires elevator deflection in the regime in which the aircraft spends most of its time is unlikely to be efficient. Thus in choosing that angle it makes sense to take account of the lift coefficient required of the tail. Where the horizontal tail surface is variable incidence, the relationship between incidence angle and lift coefficient is direct.
In your very first post on this thread, you say that "tail incidence is constrained by the desire for a minimum drag configuration at high speed" and that as a result we end up with "near-zero tail incidence". In that, there is the very reasonable premise that a wing producing lift and a tail producing almost no lift gives a longitudinally stable system.
But an inquiring mind might ask why that is the case. They might further ask whether such a situation continued to offer stability if the tail lift were to change to a small positive or negative value, or how far aft one could move the CG whilst preserving stability? They might even ask if one could have an aircraft with significant longitudinal dihedral that stable. It's those questions that this criterion is designed to address.
More importantly, I'm not sure what the new criteria is supposed to represent. Is it a criteria for stability?
Yes, it is. If the pitching moment (nose-down positive) is:
M = a*CL + b*CLt
and we're contrained to be in trim (M=0) then
dM/da = b*CLt * (dCLt/da /CLt - dCL/da /CL)
and if we require that to be positive then it leads to the criterion I quoted for CLt > 0.
dCL/da /CL < dCLt/da /CLt
You have correctly noticed, of course, that we have an issue at CLt = 0, but then it's clear from the full expression above that at that point we simply need positive lift slope from the tail surface, and if CLt < 0 while CL remains > 0, dM/da is also always positive. I'll leave you to consider the inequality for inverted flight.
Do you use this criterion in choosing the tail setting angle? Clearly not. But I do feel that it has some relevance in answering the question "Why would you design longitudinal dihedral into an aircraft?"