There was a demand for the 3e style of Fighter where it was just all feats like expanded critical and enhanced fighting style stuff. Sure, I can agree with that. It did shape the core Fighter.
I'm not sure I can agree that its why the Battlemaster fails to provide the warlord fantasy. I think I would sooner blame the fact that the Fighter really didn't lean into its core archetype and flesh it out first.
Here's the thing. The 5e Fighter walks the line between being part 3e Fighter, and 4e Fighter. Champion was the simple 3e Fighter, and Battlemaster is meant to kind of reproduce 4e maneuvers, with a few warlord-inspired maneuvers added in. Eldritch Knight was added in as a Fighter-Wizard gish hybrid option to round out the class.
That's a crappy way to design subclasses.
The Fighter's big class fantasy includes being the mercenary man, the ex-guard, the soldier girl, the gladiator. The Fighter's subclasses should have revolved around those kinds of things. Warlord should have been a core subclass that got attention. The Gladiator subclass should have had options for being flashy and using weird weapons like the net or whip. Guards should have been all about perception and putting down things without necessarily killing. Mercenary should have been a thing that had a few abilities that related to earning gold and being efficient hunters. I don't mind the Eldritch Knight subclass.
I mean, we can blame the Champion, sure. The Fighter design was so focused on threading the needle between 3e and 4e that it didn't give the warlord the weight and consideration for working within 5e framework the attention it deserved. So its kind of true. But its only a part of the story.