I would also like the possibility of "on hit" properties like Armor of Agathys to trigger on a "miss" that was an AC deflection. It's a bit counter-intuitive for such a protection to only work when you take damage, which you're trying to avoid anyway. You try to pump your AC as high as you can, which actually makes those protections not trigger.
Armor of Agathys doesn't increase AC, it gives temp HP. That's why it makes sense for a protective spell to have a damage trigger when being hit. I still agree with your larger point (or mrfuji's, I guess) that everything missing the same way should be adressed.
The idea is clearly that it chills an attacker on contact. It shouldn't matter if their weapon is deflected by armor, it's still contact just the same. The "on hit" damage shields just don't work well with the AC hit/miss system - it would be too complicated to consider misses that actually touch the target so they just made them trigger "on hit". Even though in the same system a miss can also be a hit.
That design has always made damage shields like Fire Shield unappealing to use in D&D. Wizards want to not get hit in the first place and cast AC buffing spells. Which makes the damage shields trigger less. Some are based on duration so they just become strictly worse.
The idea of a "protective" spell that requires you to take damage to work is pretty silly in the first place.
