Well do you have a better approach? I think this damage dealing approach shows pretty easily that fighters benefit from more combat rounds because they are consistent. Magic users are not consistent, they have very limited resources that - if used efficiently - can turn around situations. If they don't need to be efficient with their resources because they rest all the time of course the martials can't play out their strengths. Yes dealt damage is not the best metric, but it is the only metric we have at hand without making bigger assumptions and projections. But I think the result stays the same.
Yes, sometimes you can't enforce that, but we are not talking about exceptions, we are talking about general adventure design.
Btw, I really like your format of spoilering the anecdote, I think its a really neat idea for discussions and I will steal it
If we're just looking at combat, something every class is designed to be able to partake in, I think the main problem I have with comparing raw damage is that it assumes 100% uptime, can't account for excess damage, and doesn't account for the real metric of victory- resources saved.
Shorter combats conserve resources, so being able to kill enemies quickly is good, but you have to look at how many resources were expended. In order of importance, these would be hit points, daily resources, hit dice needed for recovery, and short rest resources.
The Fighter has excellent damage resources in the form of extra attack, action surge, and potentially fighting style and feats, though those latter two are harder to account for, given the high variance in what is taken. I've seen defensive builds snag +2 damage, and offensive builds take +1 AC from their fighting styles, and it can't be assumed that every player takes a Feat instead of an ASI, or what those Feats are (in many balance discussions revolving around out of combat proficiency for the Fighter class, people have said "well, they could take Feats to make them better at things other than fighting"- so we have to account for the fact that players might do this). Or maybe Feats aren't even used at a table!
But their resource mitigation is sharply limited to armor and second wind. Armor is something anyone can use, with varying degrees of opportunity cost, and Second Wind does not scale well (there's Indomitable but, well, yeah).
The Wizard, by contrast, has horrible damage resources. They lack the ability to alpha strike with action surge, and while cantrips scale, they don't natively add ability modifiers to their damage, and even if they did, 2d10+Int is still less than 2d6+5 x2. They could use weapons, but lacking Extra Attack, they will always fall short. There's a slight damage boost before magic weapons come into play, as there are a depressingly large amount of foes who take half damage from non-magical weapons, and the Wizard has easy access to elemental damage, but running into a foe resistant or even immune to elemental damage can also happen often, especially at higher levels of play.
So to deal damage, they have to call upon daily resources that do not scale; a 1st level spell slot to cast magic missile, for example, will always deal 3d4+3 damage. That stops being impressive very quickly. AoE spells can create impressive spike damage, but they are rarely going to slay a foe outright, so while you did hasten their demise, you aren't cutting into the damage foes deal straight away in the same way a Fighter can, by drilling deep into one foe at a time.
While it is true that shorter combats conserve more resources than longer ones, being able to severely blunt incoming damage with a non-damaging spell can be noteworthy. While daily resources are important, hit points are even more so, because when they run out, the action comes to a screeching halt.
And it's right here where we have a problem. Slow does not deal damage. We can't look at it and say "well, that's 28 damage per foe on average". Instead, Slow tells up to 6 targets that they are limited to one attack per turn, and their speed is halved, plus their AC and Dex saves are reduced. There's also a 50% chance of spells being delayed, which occasionally comes up. Slow lacks the targeting issues of fireball, as you can pick 6 targets of your choice in a large area, instead of needing enemies closely packed in for a fireball.
So we know that a successful slow makes it easier to kill foes, might prevent a foe from entering melee at all, and drastically limits the effectiveness of monsters that rely on multiattack for damage output.
If we have six foes hit by slow, 2 save on the first turn, 2 save on the second turn, and 2 save on the third turn, and they all have 2 attacks each, that one spell slot prevented the damage of 10 attacks. The only way for a Fighter to be as effective is if they can kill 5 enemies in three rounds of combat.
TLDR: in combat, the Fighter and the Wizard are accomplishing the same task, mitigating resources lost by the party, but they accomplish this in different ways. Comparing the Wizard's methods of accomplishing this task to the Fighter's and saying, "see, Fighter is superior" isn't very useful until we also compare the ability of the two classes to cast Web to prevent attacks from being made by foes.