When is equilibrium analysis appropriate?
It depends on the context.

The accepted threshold is "when everything else is slow by comparison." For example, if you have a reaction that takes place in two parts, a Jones oxidation taking a secondary alcohol to a ketone and Diels-Alder (which is far slower), you can assume for modeling purposes that the oxidation will be in equilibrium whenever you're looking at how the Diels-Alder will interact with the oxidation.

By contrast, if you're reacting something like a $\ce{CN7}$ anion (which will react very very quickly, detonating with no provocation), the Jones oxidation can't be considered in equilibrium by comparison.