"Shouldn't" is doing a lot of heavy lifting for your argument here, especially since I could easily say that "an all-martial party simply should be able to heal itself if they have a warlord."Basic HP healing is by far the most common and important kind, IME.
Thing is, an all-martial party simply shouldn't be able to heal itself other than by either taking the time to recover or - if available - by potions and the like. Were I a player in an all-martial party I'd be expecting (by 4e-5e standards) a very slow-paced and gritty adventure, with lots of rest-recovery breaks and a lot of attention paid to minimizing damage taken from any source.
If you were a player in an all-martial party in 4e, you would still have to be potentially more careful than if you had a leader with a magical power source because warlords didn't have built-in access to the sort of powerful utilities and heals that one would expect from a cleric: e.g., Cure Disease, Raise Dead, Remove Affliction, etc. The Warlord had some healing but not to the same degree as a Cleric or Bard. It was a healer but its primary benefit was tactical mastery and boosting morale.