And there we have it: ideal state for one species? the most possible species? longevity for individuals or the species?
The myth of some "natural" (the word literally means without human influence) state that is desired/better is somewhat ironic, right?
Any ideal state brings with it subjective criteria.
No, it's an "equilibrium" state, i.e. "a state of balance where opposing forces ... are equal" (from the MW definition.)
The general concept is that a stable system has at least one equilibrium state, in which no processes go out of control and potentially destroy the system.
A simple(?) example would be global warming - if the atmosphere keeps accumulating carbon, temperatures keep going up, the planet becomes uninhabitable, everything dies. Of course, that's subjectively an undesirable outcome for us - not an "ideal state", as you say - but the point is that any state in which no equilibrium can be reached (or at least approximated) exists is subject to such risks.
You could say that equilibrium is a necessary condition for an ideal state, but it's not sufficient. There can also be equilibrium states that are decidedly non-ideal, like the "everything dies" one I mentioned.
Our bodies are in a sort of equilibrium when healthy, and cancer is an example of emergence of destabilizing phenomena in the system.
Consider the Carboniferous–Permian oxygen maximum; it probably took tens of millions of years for oxygen levels to reach troublesome concentrations for plants, then tens of millions of years to return to "equilibrium."
Our current atmospheric concerns have been produced much faster, right? And I think we hope to improve the situation somewhat faster than ten million years.
My main point is that equilibrium is inherently subjective, bringing along time scales and traits that the observer cares about.
I supposed you could develop a "equilibrium for the most species at once" approach...
You originally mentioned an "ideal state". That's not synonymous with an equilibrium.
An ideal state doesn't intrinsically entail anything more than what an observer considers desirable.
An equilibrium is defined by selecting certain properties of interest, such as the timescale as you say, and once that's done, whether a system is in equilibrium can be objectively determined. There's no equivalent of that in general for an "ideal state".
"Ideal" implies normativity. Equilibrium doesn't. That's why you'll regularly find the concept of equilibrium in physics, but you won't find "ideal state" in this sense. You have concepts like an "ideal gas", but that's a simplified model where "ideal" implies a lack of full correspondence with reality in the interests of keeping the model simple.