You know that was just a very broad example of the point I was making, right? It wasn't an actual analysis of the exact numbers, or even limited to shields at all, but to the general concept of how defense can be better than offense. In any situation where you end the combat encounter with more resources, the better, even if that means the combat encounter takes longer than it would if you went full offense. That's the only point I was making.
Sure, but when someone uses numbers that do not make sense, it weakens their argument.
Anyone can skew numbers to prop up their argument. That doesn't make their argument stronger.
It's also true even taken to the extreme. I.e., even if you can kill every monster you ever face in one hit, you will end up taking damage at some point (because you won't always go first). Therefore, how long you last before you go down is limited. However, if you can prevent all damage to you, even if you only inflict 1 HP of damage per round yourself, then you can last forever and win every battle, even if it takes a long time. Forever > limited amount. I know that's the most extreme, but it illustrates the point as well.
Even your extreme example here does not make sense because again, you skew the example to match the result you want to achieve. You view it as taking your POV to its logical conclusion. I view it as nonsensical because neither offensive or defensive side can be achieved in the game as played.
On the other hand, if you use examples that match the game itself, a clearer picture can be seen. That picture is not always correct every time. As you yourself said, it is situationally dependent. But it is more clear than using numbers or situations that never happen in the game.
Let's look at level one. All 3 fighters have CON 14 or 12 hit points.
Fighter A has 16 Str, chain mail, fights Longsword and Shield, and has the Defense Fighting Style.
Fighter B has 16 Str, chain mail, fights Longsword and Shield, and has the Dueling Fighting Style.
Fighter C has 16 Str, chain mail, fights Maul, and has the Great Weapon Fighting, Fighting Style.
Fighter A is total defense and Fighter C is total offense. Fighter B is somewhere in between.
All three fighters are fighting Goblins, one at a time (i.e. the goblins are spread out throwing spears at other PCs, the fighter attacks a goblin and when finished, runs up to melee attack a different goblin). Instead of an example where the fighter always goes first, we'll base it solely on DPR per round to see how many goblins are taken out in that timeframe.
Fighter A has AC 19 and DPR 4.35 versus the AC 15, 7 hit point Goblins. The Goblins have DPR 1.825 versus the Fighter.
Fighter B has AC 18 and DPR 5.55 versus the AC 15, 7 hit point Goblins. The Goblins have DPR 2.1 versus the Fighter.
Fighter C has AC 16 and DPR 6.65 versus the AC 15, 7 hit point Goblins. The Goblins have DPR 2.65 versus the Fighter.
It takes the Goblins 6.575 rounds to knock out Fighter A during which he will take out 4.086 Goblins.
It takes the Goblins 5.714 rounds to knock out Fighter B during which he will take out 4.531 Goblins.
It takes the Goblins 4.528 rounds to knock out Fighter C during which he will take out 4.302 Goblins.
Using this simplistic example, Fighter B does the best (which is expected since he boosted both AC and damage by the largest percentage, whereas the other two boosted either offense or defense by a diminishing returns percentage), but only marginally more than Fighter C. However, the most offensive Fighter still does better than the most defensive Fighter.
The other aspect of this is that NPCs do not always attack the high AC PC. Some of them are smart enough to wipe out the non-tank PCs first. The extra AC is often only helping against a single foe and while the defensive Fighter is messing around with his foe for many rounds, the rest of the foes are using those extra rounds to attack his allies. The offensive Fighter takes his foe out quicker and then goes to help his allies (regardless of the fact that he might have gotten hit more often, as long as he has 1 hit point, he can fight).
Taking this to a more logical conclusion in game, as fights get tougher and PCs get higher level, PCs that take GWF will also take GWM and then the damage is SO much greater that Fighter B falls behind. We have all seen this in game and every analysis I have seen has backed this up. Also, the AC of the PCs will climb much slower than the to hit of normal monsters attacking, so the overall percentage of AC protection decreases the higher level the PCs become. The real defense becomes hit points, not AC.
I agree with you that offense is not always better than defense. There are many situations where that is not the case. But, one has to play the odds here. There are many more situations where offense trumps defense.
Death is the ultimate form of control (usually). The longer a fight is prolonged, the more opportunities the NPCs have to get lucky. Defensive fighters prolong fights more than offensive fighters do.
Btw, having said this, I often play melee PCs that have high AC at the expense of damage. I enjoy that style of play as a player. However, I have repeatedly seen that they do fine at lower levels, but they rarely shine at higher levels. They individually survive better, but the party tends to overall take a greater hit on resources. It's just how the game works.