In D&D armor does reduce damage. It just abstracts it into a single roll. The Armor Class system resulted from the days of Miniature Wargaming. In many games of the 60s you rolled to hit and then you rolled to see if damage was done based on the armor.
In Chainmail, and later D&D Arneson and Gygax collapsed that into one roll. The odds of actuall doing damage still was the same but now you reduced the number of rolls you needed to make by half. An important advantage in resolving miniature wargames. This carried over into the development of D&D. The d20 you roll doesn't represent the chance to HIT, but the chance to do DAMAGE. Better Armor is reflected by the reduced chance to do damage.
However as convenient this is, nearly all the gamers I know equate a single throw of the die to a swing of their weapon. It is a natural and intuitive way of visualizing what happening on the table. So it is understandable why some gamers have a dislike for how D&D portrays combat abstractly.
I myself prefer combat systems where
- An attack roll is single swing of the weapon.
- You get a defense roll based on dodge, shield, or parry
- Damage is reduced by how well armored you are.
- Hit Points are limited and even experienced character can be taken out by a single lucky blow.
Which is why I like RPGs like Harnmaster, GURPS, and Runequest/Basic Roleplaying (although 2nd edition RQ had the limbs flying a bit to readily).
The downside of my preference is that combat takes longer to resolve than D&D. In my experience about twice as long for well designed system like Harnmaster, and GURPS. So D&D has it virtues which I appreciate when running a campaign.