The problem with warlords is they didn't fit the design goals based on perceived abilities on top of not being one of the more popular classes (I base this on the public poll) and creating concerns about the level of martial healing available.
Historically, similar things like the marshal existed, simply under a different name. The healer feat does create the non-magical healer concept and it's just less than bigger healing spells. It's better than low level spells because it does have basic scaling and a large numberserker of uses. For example, healer at 20th level in a party of 4 with a 2 short rest standard is over 20 cure wounds spells worth of healing on a fighter frame.
I don't disagree that it would have been and could be possible to create a specific class. We have martial oriented classes with fighters, barbarians, rogues, monks, and rangers just like we have magic oriented classes with wizards, sorcerers, bards, clerics, and druids; both main options have already been split into several classes. The need isn't really there.
Now for desire and within the current design, I might recommend adding a battlemaster maneuver that spends one superiority to allow an ally to use 1 HD healing die without requiring a short rest, and adds the amount of the die roll to the healing. That adds more to using the feat, provides options to heal someone multiple times, and creates more effective use of the hit dice mechanics if healing is what's important to the player.
I might work on a separate class later if I have time. I don't see the need but don't mind helping other players who might want the option.