You do realize the battlemaster has numerous maneuvers that allow him to do many of the things the 3e fighter had to spend multiple feats on just to become proficient enough to have a decent chance of success in there usage.
I also realize he only gets to do them a couple of times between hour-long rests, while they were essentially at-will in 3e, and, really, in spite of the risks & penalties, things a superior combatant, like a fighter facing lower-level mooks, could get away with even without heavy feat investment.
but majority of your feats are going to one, possibly 2 builds because you need to spend multiple feats in order to be decent at most of these builds...
Yeah, feats are 'bigger.' That doesn't change the fact that the 3.x fighter had about 2.5x as many feats as baseline, while the 5e fighter has about 40% more than baseline.
The 5e battlemaster is already a multi-target multi-attacker
So's the baseline fighter, sure, it's the 5e fighter's hard-coded DPR feature, multiple attacks - but it's never as efficient to split attacks that can be concentrated, and the potential number of attacks vs multiple foes is much lower than what a 3.x fighter with GC or WWA could manage.
the battlemaster can exert battle field control through conditions, pushing & maneuvering maneuvers, the protection fighting style, sentinel feat, etc.
Sure, the few maneuvers he can do per hour exert a bit of control, but the 3.x builds that concentrated on it could do so all battle, every battle.
Could a core 3e fighter heal? Grant his allies attacks and/or maneuver them into and out of different positions? Reduce damage to himself? These and more are all things a BM can do with maneuvers...
No, the 3e fighter couldn't do stuff like that, and the Battlemater can only barely do them, very rarely, and not at all well. The 4e Warlord, OTOH, was a master of such tricks compared to which the Battlemaster is a joke, and not a funny one.
And yet with the fighter I don't have to multi-class to get spells...
Not an important distinction. In 3.x, multi-classing was always an option for the player. In 5e, it's only an option if the DM allows it. So, in both eds, you can go EK regardless. A wash.
Again...with the objective statements and nothing backing them up...
The 5e fighter is locked into the high-DPR because it always gets multiple attacks. That's it's defining feature, and it's one that's proven downright problematic in every edition, because it can be so optimal ('broken') for maximizing DPR. You can't opt out of that in favor of something else. Yes, that's an objective statement, yes, it's backed up by irrefutable fact, no, we shouldn't have to repeat those painfully obvious facts every time, just because you're inclined to be disingenuous and pretend you're unaware of them.
That's funny because a BM with Protection Style, Menacing Attack, Goading Attack, Trip Attack and/or Pushing Attack with the Sentinel Feat and the Polearm Master Feat makes one helluva defender... but yeah you keep waxing on about what can't be done with the fighter in 5e and I'll stick to actual facts.
First of all, feats are optional. No feats, a lot of that goes away. Secondly, those maneuvers are low-availability compared to the always-available feats of a 3.x fighter or combat superiority/challenge of a 4e one. That leaves you with protection style, which is dependent on a Reaction, which the 5e action economy sets a hard limit of 1 on, while a 3.5 fighter with combat reflexes could take multiple AoOs.
Yes and seeing as how most games don't go past 10th level... most of those feats were going towards building up the 1-2 things your build was centered around to an acceptable level that the BM is laready at with his scaling maneuvers...
BM maneuvers don't scale or level up, they just layer on top of his attack - they're exactly the same at 3rd level as at 10th. Really, discounting higher levels just puts the 5e fighter further behind the curve. He gets only 1 bonus feat by 10th level, for instance, and misses out on his later extra attacks, as well.
and he still gets feats. Let's also not forget a BM can retrain his maneuvers... a fighter couldn't retrain feats...that strikes me as way more customizable.
Retraining reduces the need for system mastery, sure. The 4e fighter could retrain exploits (and had hundreds to choose from, not 18) as well as feats, too, so if you want to count the 5e fighter ahead of the 3.x on this point, you'd have to count it as far behind the 4e fighter, at the same time.
The question wasn't about optimal... it was about whether the feat was needed to be adept at dealing damage... it isn't.
The 5e fighter can't trade out his DPR potential to get anything else, so, sure, it's going to be high DPR, regardless. That's part of what's wrong with it, and constrains both meaningful choice and customization. It's optimal to throw gasoline on that fire if feats are available to do so.
Just as an easy example, a fighter who trips an opponent and allows his allies to get advantage (along with every other attack he has left) is probably outputting more damage than a fighter with GWM... In other words the feat isn't necessary for a fighter to be adept at dealing damage.
All I'll say is you seem to have quite a few assumptions about how the game is/should be played...
that don't really line up with what I've seen or what some/many posters are stating.
Feats are optional, if you don't want to consider certain feats, assuming optional feats would be a valid way of factoring them out. That's not an assumption about how people actually play, just an approach you could take to analyzing the 5e fighter, if you don't want to consider things like GWM or SS.
Or you could take some non-combat feats...
So could anyone. As you pointed out, most games don't progress much beyond 10th, so the fighter is looking at 1 bonus feat, at 6th, to differentiate him from the next guy. So he's different for half the levels they're playing through, to the tune of the getting his 2nd-best-choice feat two levels early, then enjoying the advantage of 3rd-best-feat-choice from 8th-10.
Like I pointed out, above, you need a pretty large advantage for it to show up meaningfully above the noise of d20 randomness. Expertise does that handily at higher level, for instance. Special abilities that obviate checks or do things checks can't are the other obvious way to get there. The fighter doesn't get anything like that, nor is a single, 3rd-best-choice feat likely to provide it, even if the player is willing to skip optimal alternatives to take it (as, you'd have to assume a player not that interested in DPR - the only thing at which the fighter is even arguably optimal - would be perfectly willing to do).
EDIT: *sigh* The fighters extra feat in and of itself is distinct...
Anyone can take any feat. That's not distinct. So you get an extra feat at 6th, any feat you choose might be something that the next guy took at 4th, or might take at 8th.
The 3.x fighter ran into the same issue, even though he had 11 bonus feats instead of just 2, and even though he had a couple of fighter-exclusive feats. Obviously, the 4e fighter, with distinct class features and hundreds of exploits, didn't have that issue, at all (it had other issues - like being locked into the Defender role, and lacking out-of-combat options).
