The current damage multipliers probably aren't the most elegant solution, either.
I always thought that the neat thing about playing a videogame is that computers are very good at math, to say the least. It potentially allows for highly complicated algorithms for any number of variables. So long as the output continues to behave in an intuitive manner, you don't necessarily need all of the calculations to be all that simple to understand.
Along those lines, you could probably design some manner of damage algorithm that gives each weapon a variable range of damage, with your relative skill level "weighting" the results toward one extreme or another. For example, if you have a weapon that does 1-10 damage, that doesn't have to mean that at any given skill level you have an equal chance of "rolling" a 1 or a 10. An unskilled shooter would be more likely to hit a 1, but still have a chance to make a "lucky shot," and likewise an expert marksman is still going to be off-target on occasion.
Obviously, critical hits and misses go a long way toward representing that as well. But you could still have the underlying base damage calculations support this as well.
I do think there needs to be a proper balance between utilizing a good RPG system that supports the style of play Bethesda is going for, and properly representing those outcomes in an intuitive manner as well. If you're putting 30 rounds into a human being's head and they're just shrugging it off, then not only is that not fun, but the game is also visually representing one thing, while the RPG mechanics are saying another.
In tabletop games, I prefer to think of Hit Points as something more than simple structural integrity. Health, fatigue, morale, and basic willpower all factor into it, ideally. 1 point of damage doesn't necessarily have to represent the amount of tissue damage a bullet causes as it grazes your arm. A close shot can also have an effect on your nerve and coolness under fire, undermining your will to fight, for example. Likewise, a hit that takes out half your HP at once doesn't have to mean your arm is hanging on by a thread. The benefit of having a GM translate the raw output of the game mechanics into a narrative context tends to be what makes these mechanics "work."
The problem, obviously, of a videogame is that you by necessity have limited interpretations - especially visually. A bullet will either hit or not, causing either no reaction on the part of the NPC, or a blood decal hopefully somewhat close to what you were pointing at. Which leads to the issue of seeing someone hit multiple times for low damage - the visual output and the mechanical output are counter-intuitive, if not directly contradictory. And I'm not sure what the "ideal" situation could be, honestly.
There's also a potential balancing issue involved. I recall in Mass Effect 1, for example - playing that game on anything above Hard difficulty just got ridiculous. I would be blasting named NPCs across the landscape with the Mako's main turret for minimal damage. This points to there being more to making a game challenging than simply tweaking the HP values of the player and NPCs.
So, "briefly," a proper balance needs to be found in making damage as it's visually represented intuitive and in accordance with player expectations; while doing so in a manner that doesn't contradict good fundamental RPG mechanics.
I would say that while I favor skill level as a variable in the damage range of a weapon, I do feel that most of a skill's "weight" probably ought to be in relation to accuracy (ie, skill level playing a larger factor in determining whether a shot hit than how much damage it does.)