I personally believe the fluff should mean something. Something specific. If you can be a "Gladiator" just by taking a feat that has you wielding a trident and net, even though you're actually an elf wizard... then no, I think then having another Gladiator being a specific type of Fighter is inelegant. Pick one or the other. But don't have both.
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Having fluff connecting to your character should mean something.
I think you are running two things together here. And that's not necessarily a bad thing, but I think it's worth being clear about.
KM (as best I understand him) is not saying that flavour is irrelevant. He's saying that there is more than one path by which to use the PC-build mechanics to deliver a certain sort of flavour. So, conversely, when you are saying that "fluff should mean something" you're not just insisting that PC-build mechanics should deliver an outcome that has an ingame meaning, you're saying that
there should be no more than one PC-build route to a given ingame destination.
That is a hugely strong constraint that even points-buy systems have trouble delivering on, and that a class + race + feats system almost certainly can't unless - like classic D&D - we are utterly committed to strictly limiting the possible ingame destinations.
KM has made his point with reference to vampires, but I can equally make it with reference to paladins - in my game one of the paladins is built as a paladin/Questing Knight/Marshal of Letherna; the other is built as a fighter multi-class cleric/Warpriest/Eternal Defender. These different mechanical paths produce different suites of mechanical capabilities reflecting the two players' different preferences - but each corresponds, in game, to a heavy armour, hard-hitting divinely-empowered defender.
Another example from my game is the PC who started as a human wizard multi-class cleric, then retrained to multi-class invoker so he could pick up the Divine Philosopher paragon path, and then - after an ingame resurrection experience - rebuilt as a deva invoker multi-class wizard, who is still a Divine Philosopher and also a Sage of Ages. Some of the skills that the PC originally got from being a human, he now gests from feats. He use to have Thudnerwave as a wizard at-will power, but now has it as a multi-class wizard encounter power. But the PC concept in the fiction hasn't changed; it's just mixing and matching different mechanical elements to best express that fictional concept in a way that best fits with what the player wants to do with the PC.
Again, I'm not saying that this sort of flexibility is the only way to go - and of course it requires good design so that a Reaper/Slayer is not landed with redundant and mutually excluding powers, but rather becomes utterly
all about reaping and slaying (a bit like KM's Elvira). I just want to emphasise how much of a constraint is placed on both the game
and the underlying fiction that it will have room for if you go down the path of insisting on no more than one mechanical path to a given fictional destination.
I want D&D to set a benchmark for game design, not to be lagging behind in what I see as a morass of indecision.
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But a designer not making a choice and giving multiple ways for the players to work a solution? That's the definition of lazy.
Until you tell me more about your design goals and design criteria - in particular in respect of how mechanics and fiction are meant to touch one another - I can't tell what is or isn't lazy.
For instance, in the Basic rulebook for Marvel Heroic RP, Spiderman has two power-sets - a spidery one and a web-shooting one. In Civil War, though, which has Spidey in his Stark armouor, the spidery and web-shooting abilities are rolled into a single power set, and a second armour power set is added. Mechanically, this makes Spidey's iconic abilities less important - because on a single roll you can only use one item from a given powerset: so Basic Spidey can use both Wall-Crawling and Webs in the same action, whereas Civil War armoured Spidey has to choose one or the other, but can then also use a Stark armour ability.
This isn't lazy design, though - allowing Spidey's abilities to be represented and used mechanically in different ways. It's good design, because it allows the character to be powered up with Stark armour
in the fiction without leading to the game breaking mechanically in play.
Letting "gladiator" be a single feat for PC A, but a whole suite of class abilities for PC B, is a way of achieving that same sort of thing in D&D.
Why force the false choice? What's the up-side? You typically gain very little from one-true-wayism in a game as broad as D&D, and elegance is only a tool, not an end in and of itself.
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Whenever you describe someone in the fluff at your table as a gladiator, it should mean something in the story of the game, and the mechanics of the character should line up with that story.
Unless I've badly misunderstood you we're in agreement, and (hopefully) I've elaborated on your reasoning a bit above.