Themes/specialties were nothing but suggested combinations of feats. You were still meant to be able to cherry-pick feats if you didn't take a specialty as a whole.
Uh...that's not how I remember it. Specialties were originally something
everyone got, at level 1, which had various effects. Here's
the Q&A post about them (one of the few references that remain to them, due to the WotC forum change destroying all the blog posts):
"Were specialties ever considered as a means of implementing multiclassing during the development process?
In a sense, yes. I like to think of that as “soft multiclassing.” We really like the way some specialties act as pseudo-multiclassing for players who only want to dabble in the kinds of things another class does. For example, the Magic User specialty does a great job of letting any class dip its toe into the wizard’s water, without us needing a full multiclass system for that. In fact, I’d go so far as to argue that a significant portion of players who multiclass do so for thematic and story reasons, not for mechanical reasons. For those players, specialties are perfect for reflecting that thematic dabbling; it’s a dash of one flavor layered over the top of another class’s flavor. Even themes like Dual Wielder go a long way toward helping communicate that feel; a cleric that takes the Dual Wielder specialty can feel a lot more like a fighter, or even a ranger (depending on the choices that cleric makes with background and in-class decisions) without having to change classes. I think we want to keep this soft multiclassing concept while we explore ways to multiclass that are more conventional and put a bigger focus the class features as building blocks of a character."
Feats changed a lot when they decided that instead of being similar to 3e feats, they needed to be significantly larger to be on par with ability score increases, so that a player could always choose either a feat or a stat boost. However, this would have minimal effects on specialties, except the obvious rearrangement of the suggested specialties... but as a whole there could still be specialties.
In a sense, specialties were just 'feats packages' similarly to how backgrounds are mostly 'proficiency packages'.
It would be totally possible to create specialties from the feats in the PHB, and present them to players who are interested in feats but may want suggestions on a cohesive theme, so that instead of going through many pages of feats, they'd just check the list of specialties and pick one.
Well they didn't do it in the PHB, but it could be easily done and then publish e.g. a UA article.
As for an 'inspiring leader', there are many ways to do that already, not only (and not necessarily) with feats. Several Warlord-like abilities were implemented as Battlemaster maneuvers for instance, but those explicitly require to be a Fighter. Themes/specialties would have the benefit of being more generic and accessible to all.
Honestly, I think a very significant reason why the Warlord didn't show up
to the satisfaction of Warlord fans is because of the prolonged, often-reconfigured nature of the playtest.
The above podcast thing is from mid/early 2013 as I recall (and searches of forum posts here and elsewhere back me up on it)--early enough that they hadn't yet settled on the feat paradigm they were planning to use, since they're still talking about Specialties as a
thing. I think what happened was something like this:
Early pass: "The Warlord is one of the popular classes of 4e. We should include it."
Second pass: "Y'know, this is about 80% like the Fighter. We've already got this idea of Specialties--it would save a lot of space and complexity to make the Warlord a type of ally-helping Fighter with a healing Specialty. Let's do that."
Third pass: "Jeez, these Specialties are ending up really clunky, and kind of confusing for character generation. Let's just fold them into Feats and call it good."
Fourth pass: "Well hm. The Battlemaster isn't really the same as the Warlord without Specialties, but we can't grandfather them back for just one subclass..."
And then from there on out, they were in a bind--they didn't have the
time to re-create an entire Warlord class. Since they had already committed themselves to the idea that the Warlord was a special type of Fighter, they had to work within its bounds, like getting four attacks, Action Surge, Second Wind, dealing extra damage (from adding Expertise dice to most of their maneuvers or Improved Critical), etc. So they made what I would call, in 4e, a Fighter with a Warlord multiclass feat, and hoped that it would be good enough that they could tide people over until they could try again with fresh material.
The unwise nature of the "but his hand didn't grow back, hur hur" comments aside, this really reflects to me that they didn't have enough of the system nailed down for many of the commitments they were making for classes until far too late in the design cycle--and the warlord fell through the cracks as a result. I mean, they even literally say, right in that podcast, that the "tactical fighter"
isn't enough unless you add that specialty. If that's not the closest we'll ever get to a developer
directly saying 5e doesn't have a..."complete," if you will...Warlord in it, I don't know what is.
Edit:
In fact, in reading over all of this...I really,
really get the feeling that they were hanging a great deal of the 4e-related stuff on the Specialties mechanic ("Defender" specialty, talk of making a "Leader" specialty...), only to drop it later on, so late that they couldn't come up with a suitable replacement in time. Because with Specialties in the mix, it sounds like you could quite easily have a Fighter who gives attacks to other people, inspires allies to greater heights, and (potentially) even heals allies through stirring words and exhortations. Now instead, all of that gets condensed into granting a buffer of THP (IMO relatively slim, at least after level 3 or so), or spending money in the form of Healer's Kits to restore 1d6+4+level HP per rest (requiring 2 feats to do so).
More or less, I think that they saw that 90% of the Specialties were just overcomplicated pre-bought feats, so they eliminated the idea...but that remaining 10% was a cost. Whether they accepted that cost and planned to address it down the line, or were unaware of it and have needed that time to come up with a solution, I don't know. But it certainly sounds to me like
that is where the TCM and the other 4e-centric mechanics went--sucked into the removal of Specialties.