I can't follow your shifting arugments. Just above, you said that comparing the fighter to the sorc in a pure DPR-off had the sorc showing the fighter up, which takes almost all of the sorc's resources to do.
That's someone else's numbers, I'm leary (I expect they're actually closer to parity on a reasonable analysis) but I'll accept them for the sake of argument.
Now, though, you're saying that the closer you get to a DPR-off, the better the fighter looks?!
Yep. The fighter is a very DPR-focused design, it's best features work best when devoted to delivering DPR, it'll put in it's best showing in such comparisons. When that's not good enough, it's a very bad sign for the fighter.
You also say that when a sorcerer is using slots for other-than-DPR, this also shows up the fighter, but just above you poo-pooed fighter non-DPR contributions because they really didn't have any. If that's the case, the Sorcerer using his slots in fields the fighter is already weak in (ad argumentum) doesn't really continue to show up the fighter, does it.
'Show up' by such a large margin the fighter's not even really in the running, sure. If you want to compare classes over many dimensions of contribution rather than focusing on DPR-as-King, the fighter will loose a lot of such comparisons by very large margins, indeed (as will the Sorcerer to the Wizard or Bard, likely) - you're prettymuch back to shaking down the Class Tiers, with that kind of analysis.
You seem more interested in preserving the conclusion that discussing the premises.
There's a conclusion?
Zapp's conclusion is that the fighter 'needs' GWM/SS.
If DPR really were 'king' that'd be less likely the case, as mere parity in DPR would be all anyone needed - since versatility would be valued at nil, the only thing having other things to channel your resources to than DPR would be 'traps.' The fighter would be downright dominant, and cutting GWM/SS would be a safe call.
My argument is that in a holistic review, fighter does very well on DPR because it has the class features to stick in and deliver it consistently, while a few other class builds can, on paper, outgun the fighter, they do so by ignoring their own niche and abilities and so degrade the party ability to succeed in a rounded adventure setting. A slavish focus on DPR would leave you twiddling your thumbs in much of my games and even, at times, find yourself frustrated in combat because the objective wouldn't be to reduce hitpoints as fast as possible.
Nod. It's a straightforward balancing act. The fighter has little to do outside of tanking away in combat and grinding out the DPR. As long as he's better than that by some margin, it makes up for all the times he's 'twiddling his thumbs.' The margin depends on the emphasis on combat over social/exploration, and, in combat, on DPR over other factors. The more important DPR, the narrower the margin the fighter needs to balance - but, unless DPR really is King, he needs /some/ margin of advantage in that area. The more 'holistic' and varied the campaign, the larger the advantage the fighter needs in combat to really shine bright enough when he has the opportunity to do so. If you have weeks of painstaking exploration and cunning politicking, then, finally a battle one day, and grinding out DPR is the only thing that matters, that day, then more versatile classes can go all-in on that - the fighter /still/ has to beat them in that case, and not by a small margin, to seize his rare chance to shine.
It's a delicate balancing act, really, and, while for the sake of argument, I'm willing to accept the theory and discuss it's implications (like "Fighters 'need' GWM/SS to get enough DPR to balance"), my personal opinion is that it never really works. The DPR character is either irrelevant and overshadowed, or downright OP and game-wrecking. There's a shifting DPR threshold and he's either on one side of it or another, it never actually balances. It's just too specific, yet too critical, a contribution to use as a prime, let alone sole, balancing factor for a character, let alone a whole set of sub-classes.
1- He can also have far more durability with improved AC, HPs, autoheals using a BA and better saving throws.
'Meh' on all counts. The hp advantage is 1/level. AC can be cheesed up in a variety of ways. IDK what BA has to do with healing, but Second Wind trails off in importance rapidly. And 'better' saving throws? The fighter is STR/CON, the sorcerer CON/CHA. In both cases, CON is the more important save, and CON a second-priority stat, while the less-important save maps to the primary stat (setting aside the otherwise very effective DEX-fighter builds, like the Archery SS). STR saves come up more often, but they're usually for comparatively minor effects, while CHA saves keep you from, for the major instance, being dominated (which, with a DPR build, is nice for your party).
2- It's not only about casting high level spells, you also have to defend yourself, when I played a sorcerer I burned a lot of slots on shield, blur, mirror image, etc. You also want your area spell, perhaps a teleportation spell, buffs...
Yes, even the Sorcerer has considerable versatility. He /can/ put a lot towards DPR, or he can put it towards defense or whatever else he knows a spell for... he can't compete with the Wizard, but he's got it all over the fighter, that way.
Yes, but don't compare a sorcerer that can not be attacked fully buffed expending all their sorcery hit points, metamagic extra damage from class, etc to a fighter only using his normal attacks.
No problem, compare that sorcerer to a SS fighter who can't be attack and is fully buffed and expending all his limited resources on DPR. Fair's fair.
If you allow multiclassing you can also be a fightlock, warter or whatever is called.
"Waste of time" I suspect.

But, sure, maybe a Champion/Berserker or something? I mean, you are delaying or even losing extra attack by MCing out of fighter, and in a weapon-based DPR build that's not such a great idea, but MCing should certainly be open to both.