The only lesson I see to be drawn from the Philippine-American war is that a disorganized, poorly equipped, untrained insurgency with no external support and no supporting theory, example, or precedent for effective guerrilla warfare can be roundly defeated by an army with almost infinite military superiority and the will to use unrestricted violence against combatants and non-combatants alike. That's not exactly news, and I don't know how relevant that lesson is to any modern conflict, as modern conflicts are generally not fought under those conditions.