When you say "people" do you mean "all people" or perhaps "some people"? I am a person, and I've never had trouble wrapping my brain around it, and have never had to shake my head. "Damage on a miss" means that, for that player playing that PC doing that thing, the default failure condition ("miss") is instead a partial success condition. It's player fiat.
I'm sure there are people who can't make sense of that, but then for any interesting thing X there are at least some people who can't make sense of it. That doesn't necessarily tell us much about the worth of X, though.
As a question is it damage on a miss that is the major sticking point or killing on a miss or both equally?
I could never get my head around it in 4E and it was one of the reasons we gave up playing that edition. I put it in the same category as Evasion for Rogues in 3E as I've grown to dislike that too, but then I've been playing for 30 years.
Holy cow, no it wasn't. Where do you even get this nonsense?
In 4e, attacks and spells are normalized into a unified system, so the actor always rolls for success. Before 4e, most spells had saves and most attacks used attack rolls. In 4e, it's all the same unified mechanic.
So in 4e, instead of the target making a reflex or "spell" save against fireball, the wizard makes an attack vs. Reflex. Instead of half damage on a successful save, it's now half damage on a missed attack. Same exact process, same exact logic, mathematically reversible, but now the "aggressor" makes all the rolls for consistency. Half damage on a miss is born. There you go.
The real question is if you remove it, what replaces it?
The point of weapon DoaM is to give great weapons a bone since you can miss and you dont get the extra attack of TWF or shield bonus to AC of S&S, or range of Ranged and Reach weapons.
So do yo go back to "Swing, miss, end turn" for heavy weapons?
Do we give Two Hander Style its own Reckless strike?
Do we give them a second attack as a backhand swing?
Do we give them more accuracy?
Do we give them even more damage to make up for missed??
Do we give them an effect like knock back?
What do we do?
People complaining but no solutions.
I myself don't care, as long as it is not simply a reduction in the options available, in which case it would be actively disappointing. It would also be disappointing if the designers are being swayed by a vocal minority, which may be the case.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.