Yes, children are trained as squires to become knights, sent off to monastery to become clerics, apprenticed to a mage to become wizards, etc. Most classes at level 1 are modelled on the heroic output of in-game professional training + natural talents. The warlord class has no equivalent in-game meaning and feels artificial and arbitrary in-game (outside of the metagame). A child trained as a squire to become a knight may evolve to be a warlord, but a child is not thrown into Warlord Academy. Warlord IS a mantle earned by anyone with the right stripes and experience, and 4E warped the 'warlord' concept to fit into an artificial gamist framework.In AD&D, and even moreseo in 3E (with it's easy multiclassing) class is a reflection and expression of some ingame state of affairs. And on this approach to class, it doesn't make sense to have a class and class features that don't accurately express some feature of the ingame reality. So a 4e warlord class wouldn't make sense.
But in 4e classes are best seen as "metagame packages/bundles" first, which then determine some ingame state of affairs - but they don't themselves express any ingame natural categories. So whereas, in AD&D and 3E, "fighting men" and "magic-users" are part of the ingame reality, in 4e there are only warriors in the gameworld - fighters, warlords and STR-rangers are simply various metagame devices for playing a warrior in mechanically distinct but balanced ways.
In my ideal 4E, you can only build a 'warlord' using any base class and the right abilities and power selection. Take a knight class and add some tactical powers. Take a cleric and add some inspiration powers. But don't fabricate a warlord class out of relatively thin air and call it a 'warlord'. Creating a warlord class to fit the predefined roles is about as arbitrary and gamist as 2nd edition Outer Wheel designed to personify the 9 old alignments. Take away the old 9 alignments and the Outer Wheel collapses on itself, its gamist spine torn out, with no tangible in-game justification left to support itself.
Furthermore, if this was just about the warlord, it wouldn't affect my view of 4E as a whole. But as I described before, I see many, many other failures of internal logic between crunch and fluff.