Exactly as modern, tenuous, and inappropriate an objection, yes.
Much more modern, tenuous, and inappropriate an objection, compared to warlord, actually.
Warlord has never been broadly used in Modern English in a positive light. Modern English is being used as a proper noun, here, rather than referring to the English spoken in today's society.
Naming a heroic class (or one with simply neutral moral implications) Warlord would be like renaming the Wizard "Warlock", and burdening it with confusing negative connotations that have nothing to do with the class being described.
Warlock works for the Warlock, because the idea is that Warlocks have transgressed to gain their power. They have formed pacts that sensible and morally upright people would
at least look down upon. That makes the name entirely appropriate. In pop culture, Warlock is pretty much never used to refer to someone who is unambiguously Good. If it were, it would be weird. Maybe in a way that's interesting and tells a good story, but weird nonetheless.
The Marshall-Captain-Mark-Leader-Person is not intended to have a negative connotation. Their name should therefor be neutral in terms of ethical assumptions about someone labeled by the name of the class, in the popular conception of someone reading the book.
And as for John Carter, I hate to break it to you, but those stories aren't all that popular anymore. I'd be willing to bet actual cash money that at least twice as many potential DnD players think of real world warlords, and historical military tyrants they resemble, as think of a John Carter story, when they hear the term "warlord".
It's not about editions, Tony. I love 4e, and want the class brought back in a satisfying manner. The name is bad, though. It needs a new name.