The thing is the base (a martial bonus giver) covers a wide variety of concepts:
1. Let's go for the classic example: Julius Caesar. A 43 year old politician turned warrior that laid the foundation of the Roman Empire.
He sure as hell wasn't a fighter.
2. A Rescued Princess/Prince that gives bonuses to their party while getting into peril.
3. A Kobold mascot, whose dapper attitude makes him/her adored by all.
4. An singular Ōendan with a set of flags that cheerleads the rest of the team to victory.
5. and of course, the classic
Yes you could make the argument that his super soldier serum makes him a fighter, but in a world where you have hulk and thor on the team, his biggest advantage has always been his charisma and his leadership skills.
all of these concepts can be done with the warlord, and even if you prefer a title like captain or cheerleader instead, it doesn't change the base conceptual model of the class.
One of the great things about the warlord class in 4e as it created a real agony of choice with the cleric.
If you took a cleric, you had greater healing abilities.
If you took a warlord, you might be able to shave a round or two off your fight, saving more hp then the cleric could heal.