This obviously leads to the ages-old problem of making the Fighter some sort of super-broad parent class and the other melee archetypes super-specialized ones. Which, sadly, is the reason Fighters tend to be terribly weak in most D&D editions.
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Fighters should be as rare as Rangers and Paladins: they should be the elite troopers, the battle hardened veterans, the sword saints, and if no room for the Warlord is left, then also the generals and the commanders. If the definition of the Fighter is "anything with a sword that isn't a paladin, ranger, barbarian or rogue", then you have an archetype that probably doesn't deserve a place in a class-based system.