As has been noted - that goes both ways. You don't like damage on a miss? Don't play a character that uses it! Done.
Arguments of the form, "you cannot have the option in the game for you to use, because I don't like it" are not terribly reasonable, in my opinion.
This isn't a particularly good argument because DoaM is not a class feature, it's a mechanic. It's a mechanic that's typically found in a class feature, yes, but it's not limited to that one mechanic.
Back in the playtest when DoaM was part of the fighter it was also part of several monsters. Which makes it trickier to avoid because you can't just forgo that class.
Saying you can ignore DoaM by ignoring the fighter option that had it is like saying you can currently ignore "reroll 1s" by not taking the current version of the GWF. Which just does not work as rerolling 1s could appear anywhere in the game.
So, if the class or concept is about someone that is well modeled by DoaM, what then?
I'd love to hear an example.
I am pretty sure you are wrong here. He's not looking for a contingency for a bad night of rolling. He sees a character concept that seems to be a notable disadvantage, statistically speaking, such that his players avoid it. He'd like to see an option (just an option, not a mandatory feature) be available that would negate the disincentive to play the type.
If that were the only factor then it would have an easy fix to give the option any other mechanic with the same effective result: a boost to average damage. Which is what they did for the final book. GWF now have better average damage than other fighter options and their minimum damage on a hit is much higher. They're actually pretty solid.
And yet... the discussion continues. Because the discussion isn't about DoaM but the nature of hit points and an edition war based around a common 4e mechanic being sidelined. DoaM is just an excuse. It's a proxy edition war. The Vietnam of edition wars.
A GM of my acquaintance saw a tendency in his gaming circles. It was in respect to plots centered around a character, but it holds for other aspects of RPGs as well. It goes like this: Your character has a pony. It is a good pony. You like it. Some other character is given a pony.... and you start feeling like somehow the other guy having a pony makes your pony worth not as much. You start arguing that other people shouldn't have ponies. You having a pony isn't good enough for you - other people need to *not* have ponies, for you to be happy.
This is, obviously, kind of silly. The existence of other ponies does not diminish your pony. The attitude is dysfunctional, and leads to you arguing for making the game less fun for others.
You sound like this - as if the game can only have the stuff you like, and not stuff that others might like, even if that other stuff really doesn't impact you.
It's a little more complicated than that because...
Okay, I tried to write my reply following the metaphor and it's gibberish. So I'm abandoning that and trying again in plainer text.
I'm all for people having game elements they like, especially when they're options that can be added or removed. That's cool. I'll support variant rules and options that give people something else they like. (Heck, as I've demonstrated , I'll even spend an hour writing them.)
And I'm all for the base game not being entirely what I want provided I can also be given options that let me modify the game. That's fair.
However, this works best when the rules and options to be modified are the core rules and not class options. Mostly because it's a single change versus a variable number of changes. It's easy to change how rests work or hit dice recovery works as most of that is class independent. The more you need to read class features, monster powers, feats, and the like the harder it is to implement the change.
For example, critical hits. Let's say I don't like the base method of crits in 5e. I want something more like 4e with max damage, so rolling snake eyes doesn't result in a crit that's less than average damage. Seems easy enough: max damage on crits. However, a number of classes have features that modify critical hits. So now I need to go through those options and make a ruling for each. To say nothing of monsters.
This is the big difference between a regular RPG and an RPG designed to be modular.
As such, including a mechanic in the base rules that is divisive is... problematic at best. Especially one that would have ended up in the Basic Rules.