Chiquitafajita, the idea that HP stay relatively stable but that the damage you take depends on the relative abilities is exactly produced by Tunnels & Trolls. (In that game, CON = HP.)
Since you know the Troika! system (which is an adapted version of Fighting Fantasy, which derives a lot of mechanics principles from Tunnels & Trolls), I can explain it this way: Imagine that the damage done in Troika! is not based on a secondary roll, but is the difference of the combat totals between the two sides in a fight.
Instead of rolling for damage, you produce a total (in Troika!, 2D+Skill+Special Skill), and the winner inflicts the difference in damage upon the loser.
In Tunnels & Trolls, the number of dice used is based on the weapon, not a fixed 2D. In T&T, you figure “dice + adds,” but each T&T weapon is worth a certain number of dice, heavier weapons doing more (but having STR and DEX minimum requirements–something borrowed in The Fantasy Trip). Your adds are derived by totaling each point of STR, DEX, and LUCK over 12 (on a 3d6 system modeled on OD&D), like stat bonuses in D&D but added up beforehand. So, say, STR 13, DEX 15, LUCK 10 gives +4 adds onto the total from the weapon.
The brilliant thing in this system is that group combat can be handled by everybody’s total from one side versus the grand total from the other. The difference in the collective total is damage done to the losing side that round, divided up between them.
Fighting Fantasy (and hence Troika!) don’t do this because the number scales are smaller, but it’s possible to wiggle things to make it work this way, depending on how much you want the choice of arms and armor to matter in strategic prep for combat-oriented characters.
About hit points, Jon Peterson traces their background to a 1972 Gygax and Arneson collaboration, rules for naval combat called Don’t Give Up the Ship. Ships can take multiple hits before they sink (so have hit points) and damage done varied according to the caliber of the cannons. You roll a die for each “fire factor” calculated on the basis of the caliber of the guns in an inter-ship attack. These principles were transferred to D&D. Why a sword should do variable damage is not clearly stated, but I guess it represents “direct hits” versus glancing blows or scratches. The point in common between ship-to-ship naval warfare and warrior-to-warrior melee combat is that both represent individual units around which the whole game pivots: big ships and big heroes. When one goes down, the game is “over.” For both, “zooming in” to look at damage close-up, and allowing the dice to provide twists of fate, seems to be the common feature.
I agree that it’s a design choice too little examined. Why not have more “saving throws” against fixed damage instead of assailants’ rolls for damage done, to keep characters from dying instantly? You can just say every blow is fatal unless the figure struck makes a roll, with various outcomes as a result (shrug it off > various degrees of wound-induced penalty > permanent injuries > death). Then you get rid of hit points and damage rolls, but figures roll to resist injury. This way lies Ars Magica and its “soak” roll.
It may be the feel of it. People like to be involved in how good their hits were, and that means rolling for the damage they themselves inflict.