Some people also argue that having a warLORD at level 1 makes no sense, like having a lvl 1 mage called an archmage.
In 1e, a Warlord was a fighter, around 8th level, IIRC. Also in 1e, a Wizard was a magic-user of 11th level. Wizard denotes a level of experience and mastery far in excess of what '1st level' implies, but it's a class name. So, for that matter, do sub-class names like Knight and Champion. Rogue, which was something like a 3rd or 5th level Thief in the olden days, is about the lowest-level modern class name.
So I think the class should have a name that reflect this power progression (lets say Marshal, with the capstone being called Warlord), and have archetypes based on being better prepared for battle.
Marshal suffers from the phenomenon much worse than Warlord, which, at least, isn't a formal military rank and doesn't carry legitimac, while a Marshal is a high-ranking field officer - or an old west law-enforcement official, which is worse.
Plus, the Marshal was a terrible class from the nominally-3.0-compatible battlesystem.
I think we should try to separate the 4e warlord from what we want of the 5e warlord. I'm okay that in 4e, the warlord was a healer, but what if, maybe, in 5e he was to do something else?
5e class design isn't constrained by formal Roles like 4e's was. In particularly, there's no 'controller' role in 5e, classes like the Cleric that in 4e were leaders get plenty of 'controller' powers and blasting in 5e. There were a few really nice Warlord exploits that shaded into controller functions, influencing enemies though tactical manipulation or intimidation, for instance - the 5e Warlord could delve further into those, as well as covering the inspiration- and tactics- based support contributions the 4e Warlord was specialized in.