It's not really the same thing though, for Aoe spells, like Fireball, that engulf entire areas and your character is definitely inside those areas. I defy anyone in the midst of a massive explosion to not even get a single scratch on them, even a bruise or a scrape from some debris.
Weapons either hit you, or they don't. If they do hit you, maybe they don't hit very hard? Fine, that makes sense. But if they don't hit you, because they missed you, that's not the same as saving throws giving 1/2 damage and not being able to have no damage.
There is nothing comparable between a fireball and an axe. Fireballs area of effect auto-hits, so 1/2 damage-on-a-failed-save is not equivalent to damage-on-a-miss.
You seem to keep bringing up that "point" without ever actually reading or trying to understand why it's invalid and not comparable. Spells auto-succeed at targetting their area of effect. Whether that's a person, a location, whatever. That part is "auto-hit". You aren't targetting a person with a fireball, you're targetting a place. Think of it like a mortar cannon with a big explosion. Some guys in the blast radius will be blown to bits, and others will manage to duck out of the way of most of the energy which is not distributed uniformly.
The two issues are not the same, which I brought up in my points. Hitting or missing, is both a binary proposition in D&D rules, as well as in real life. Hitting is necessary but not sufficient to deal damage in real life, but it is in D&D rules. However, the same cannot be said about missing with a sword in real life, and no attempt is made to explain how a weapon can harm you if an attacker misses you.
Just saying "abstraction" does not prove anything. The definition of hit points in this packet aren't even self-consistent. On one line they say no weapon connections are made at all with your body until the one that kills you, then in the very next line, it says when you at 1/2 HP and below you exhibit signs of cuts, scrapes, wounds, etc. They can't even get their own nonsensical "abstract" definition consistent with itself.