I'm shamelessly quoting from 4e here, but I think the following applies in most (non-mechanized) RPG's at least to some extent.

Hit Points

Over the course of a battle, you take damage from attacks. Hit points (hp) measure your ability to stand up to punishment, turn deadly strikes into glancing blows, and stay on your feet throughout a battle. Hit points represent more than physical endurance. They represent your character’s skill, luck, and resolve—all the factors that combine to help you stay alive in a combat situation.

If Hit Points are abstracted in this way, then damage must be too. Static damage doesn't necessarily mean the same exact slice or the same exact bruise inflicted on the target. The first 5 damage might be a club swing that bounced off the fighter's shield, but weakened his arm a little bit. The next 5 damage could be an actual connecting blow that left a mark. Really, 5 damage could even be a complete miss. The fighter could avoid a swing altogether, but got a stitch in his side as he wrenched out of the way. So even "inept hits" can do "damage".

Again, I'm using 4e here, but the issue of randomization is covered in which dice are used for the damage roll. Two dagger wounds aren't going to vary much from one another, hence a 1d4 is used. Two greataxe wounds could be very different, and thus we have the 1d12 for greater variance.

I guess what I'm saying here is that static damage doesn't really differ from variable damage in terms of what you'd see happening in the game world. It's just a rule difference to make combat go more smoothly for certain repetitive attacks, and more exciting for those important hits.

EDIT: I was thinking back to my time playing AD&D. I don't know how many RPG's use this model, but AD&D used 1 minute rounds. This also abstracts how static damage would be perceived in the game world, though in a different way. We can remove the Hit Point abstraction altogether and assume that 5 damage really means 5 "points" worth of physical harm to your body.

So sure, the critter might do the same amount of bodily harm to you each round (on average), but we are dealing with minutes here. That indicates that it wasn't from just one blow, but rather a series of glancing blows, solid hits, and misses. The weapon properties don't necessarily have anything to do with it. It's just the cumulative amount of punishment that went out over the minute.

Use adamantine arrows to bypass appropriate damage reduction

As you've noted, the primary purpose of the special material adamantine seems to be damaging objects, yet adamantine arrows are typically a lousy choice for, for example, destroying a dungeon wall. But that's not all the material's good for. The universal monster ability damage reduction says

Some monsters are vulnerable to piercing, bludgeoning, or slashing damage. Others are vulnerable to certain materials, such as adamantine, alchemical silver, or cold-forged iron. Attacks from weapons that are not of the correct type or made of the correct material have their damage reduced, although a high enhancement bonus can overcome some forms of damage reduction.

An archer will want a batch of adamantine arrows if, for example, confronted with a gemstone gargoyle or a creature that's the subject of the spell stoneskin. While some archers bypass DR/X (adamantine) using a bow with an enhancement bonus of +4 or better, not all archers are fortunate enough to have such a weapon.